short cut for maths.docx

8/14/2019 short cut for maths.docx

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Squares

Here are the Squares of 1 to 30 numbers. Byheart them....

1 x 1 = 1

2 x 2 = 43 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

7 x 7 = 498 x 8 = 64

9 x 9 = 81

10 x 10 = 100

11 x 11 = 121

12 x 12 = 144

13 x 13 = 16914 x 14 = 196

15 x 15 = 225

16 x 16 = 256

17 x 17 = 289

18 x 18 = 324
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19 x 19 = 361

20 x 20 = 400

21 x 21 = 44122 x 22 = 484

23 x 23 = 52924 x 24 = 576

25 x 25 = 625

26 x 26 = 67627 x 27 = 729

28 x 28 = 784

29 x 29 = 84130 x 30 = 900

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Cubes

Here are the Cubes of 1 to 15 numbers. By heart them.....
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1 X 1 X 1 is : 12 X 2 X 2 is : 8

3 X 3 X 3 is : 27

4 X 4 X 4 is : 645 X 5 X 5 is : 125

6 X 6 X 6 is : 216

7 X 7 X 7 is : 343

8 X 8 X 8 is : 512

9 X 9 X 9 is : 729

10 X 10 X 10 is : 1000

11 X 11 X 11 is : 133112 X 12 X 12 is : 1728

13 X 13 X 13 is : 219714 X 14 X 14 is : 2744

15 X 15 X 15 is : 3375

SEARCH YOUR TOPIC HERE.........

T H U R SD A Y , D E C E M B E R 2 2 , 20 11
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Shortcuts in Multiplications

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NOTE : These techniques are for Mental Maths. You should do calculations

in your mind only. Please avoid using Pen/Pencil and Paper.

Multiplication using multiplesAssume that we should find out the result of 12X15.12 x 15 (Here we can write this 15 as 5x3)

= 12 x 5 x 3 (now 12x5 becomes 60)

= 60 x 3 (For this you just calculate 3x6, that is 18 and add one Zero to it. thatis 180)= 180 (see, how simple it is?)

Multiplication by distribution

Assume that we should find out the result of 12x1712 x 17 (Here we can divide this 17 as 10+7. here, multiplying 12 with 17 is

same as multiplying 12 with 10 and 7 separately and then adding the results)so, we can write it as= (12 x 10) + (12 x 7)

= 120 + 84= 204
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Multiplication by "giving and taking"

12 x 47 (Here its little difficult for us to calculate the multiplication of 12 and

47 mentally. so just check for the ROUNDED number nearer to 47. Yes it is

50. so.....

= 12 x (50 - 3)

= (12 x 50) - (12 x 3) (we have discussed this rule earlier)

= 600 - 36= 564

Multiplication by 5

* If we have to multiply a number with 5, just divide the number with 2 andthen multiply the result with 10. Confused? Its very simple step actually....

428 x 5 (Now just divide the number with 2)

= 428 x 1/2 = 214 (Now multiply it with 10. I mean just add a zero at the end

:P)= 214 x 10= 2140 (This is our result)

Whats the logic behind this step?

Very simple.* Lets say the number is X.

* Now we are dividing the number with 2. so here X becomes X/2.* And then we are multiplying it with 10. So it will become 10x / 2

* Now cancel it with 2. so it becomes 10x / 2 = 5X = 5 multiplied by X. Thats it ;)

Multiplication by 10 ------------ just move the decimal point one place to the

right

16 x 10= 160

5.9 = 159169.93 = 169.3 (Need an explnation for this too??? :P)

Multiplication by 50 ------ divide with 2 and then multiply by 100


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Well, this is also same process as we did for 5. Here we should add an extra

zero. Thats it

18 x 50

= (18/2) = 9

= 9 x 100= 900

Multiplication by 100 -------- move the decimal point two places to the right

45 x 100

= 4500

Multiplication by 500-------- divide with two and multiply with 1000

21 x 500

= 21/2 x 1000= 10.5 x 1000

= 10500

Multiplication by 25 ---------- use the analogy Rs 1 = 4 x 25 Paise

25 x 14 (just divide the 14 as 10+4)= (25 x 10) + (25 x 4)

= 250 + 100 ---> Rs2.50 + Rs1= 350

Hey one more thing. Here you can use another technique too. Which we have

used for multiplication with 5.

Multiplication by 25 ----------- Divide by 4 and multiply by 100

36 x 25= (36/4) x 100

= 9 x 100= 900

Multiplication by 11 (if sum of digits is less than 10)


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72 x 11

= 7+2 =9, it is Less than 10. so,= place this term 9 between 7 &2

= 792 (That's the answer)

Multiplication by 11 (if sum of digits is greater than 10)

87 x 11=> 8 + 7 = 15

because here 15 is greater than 10, first use 5 and then add 1 to the first term 8,

which gives you the answer

= 957

Multiplication of numbers ending in 5 with the same first terms (square of anumber)

25 x 25first term = (2 + 1) x 2 = 6

last term = 25

answer = 625 ---> square of 25

75 x 75

first term = (7 + 1) x 7 = 56

last term = 25answer = 5625 ---> 75 squared

Read more:http://www.gr8ambitionz.com/2011/12/shortcuts-in-

multiplications.html#ixzz2ifVHZOZ5


Additions ShortcutsAddition of numbers close to multiples of ten (e.g. 19, 29, 38, 59 etc.)

This technique is useful for Mental calculations
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116 + 39 (Here we can write this 39 as 40-1)= 116 + (40 - 1)

= 116 + 40 - 1

= 156 - 1 (Instead of adding 39 to 116, we just add 40 to 116 (because we can

do this without using pen and paper) and later we subtract one from it)= 155Try this.. This is very useful tip while doing calculations.

Now lets try another example.

116 + 97= 116 + (100 - 3)

= 116 + 100 - 3 (Here, instead of adding 97 to 116, we are just adding a 100 to

116 and then subtracting 3 from it :)

= 216 - 3= 213

Addition of decimals12.5 + 6.25

= (12 + 0.5) + (6 + 0.25)= 12 + 6 + 0.5 + 0.25 (Here we just added the rounded numbers first and later

we added the decimal numbers :)= 18 + 0.5 + 0.25

= 18.75
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SUBTRACTION BY NUMBERS CLOSE TO 100, 200, 300, 400, ETC.250 - 96= 250 - (100 - 4) (here, instead of subtracting 96 from 250, we are

just subtracting 100 from 250 and then adding 4)

= 250 - 100 + 4 (Why adding? because the actual amount we have

to subtract from 250 is 96. but we are subtracting 100. That means, we

are subtracting 4 numbers more than we actually deserve. so our 250 will feel

bad. so we should add that 4 to it:)= 150 + 4

= 154

250 - 196= 250 - (200 - 4)

= 250 - 200 + 4 (here also same. In order to subtract

196, we subtract 200 and adding 4)= 50 + 4

= 54

Note : We can use this logic for any number. According to our convenience.

Lets see,

216 - 61 (Here i found it difficult to subtract 61 from 216)

= 216 - (100 - 39) (So i just decided to subtract 100 to it and later will subtractthe extra 39)= 216 - 100 + 39 (Hey, see here. How about writing this 39 as 40 -1 ?)

= 116 + (40 - 1) (dont be confused. just practice this method and you will come

to know how easy and efficient method it is :)= 156 - 1

= 155
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Subtraction of decimals

47 - 9.9 (How about dividing this 9.9 as 9 + 0.9 ??)

= 47 - (9 + 0.9) we can write this as...

= 47 - 9 - 0.9= 38 - 0.9= 37.1

18.3 - 0.8

= 18 + 0.3 - 0.8

= (18 - 0.8) + 0.3

= 17.2 + 0.3= 17.5

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html#ixzz2ifVXerS9



T H U R SD A Y , D E C E M B E R 2 2 , 20 11

Shortcuts in Division

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There are so many types of divisions are there. Lets have a look.

Division by parts --> Imagine you have Rs.874 . You have to give that to your

two children.874/2 [We can write this 874 as 800+74 (for our convenience)= 800/2 + 74/2
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= 400 + 37

= 437

Division using the factors of the divisor: "this is also called as Double

Division"70/14

= (70/7)/2 (Because 7 and 2 are the factors of 14)= 10/2

= 5

Division using Fractions:132/2= (100/2 + 32/2) ( here we've broken the given fraction into

two separate fractions)

= (50 + 16)= 66

Division by 5 :Note: if you have to divide any number with 5, then divide it by 100 and then

just multiply by 20

1400/5= (1400/100) x 20

= 14 x 20= 280

Division by 10 (Its very simple, just move the decimal point one place to the

left)

0.5/10= 0.05

Division by 50 ( Just divide with 100 then multiply by 2)2100/50

= (2100/100) x 2= 21 x 2
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= 42

700/50= (700/100) x 2

= 7 x 2= 14

Division by 100 (just move the decimal point two places to the left)25/100

= 0.25

Division by 500 (just divide with 100 and then multiply with 0.2)

17/500

= (17/100) x 0.2

= 0.17 x 0.2= 0.034

Division by 25 (just divide by 100 and then multiply by 4 )500/25= (500/100) x 4= 5 x 4= 20

750/25= (750/100) x 4= 7.5 x 2 x 2= 30

Read more:http://www.gr8ambitionz.com/2011/12/shortcuts-in-

division.html#ixzz2ifVjfXF4


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SA T U R D A Y , D E C EM B E R 2 4 , 2 01 1

Decimals

Some times, you have to convert or express the given percentages in the form ofdecimals. It is not such a difficult task as we think. Have a look at the following.

1% = 1/100 = 0.01 (if two zeros are given, just move the decimal pointer twoplaces left)

2% = 2/100 = 0.02 = 1/50 (the simplification of 2/100)3% = 3/100 = 0.03

4% = 4/100 = 0.04 = 1/25

5% = 5/100 = 0.05 = 1/20

6.25% = 6.25/100 = 0.0625 = 1/167% = 7/100 = 0.07

7.5% = 7.5/100 = 0.07510% = 10/100 = 0.1 = 1/10

12.5% = 12.5/100 = 0.125 = 1/820% = 0.2 = 1/5

21% = 0.2125% = 0.25 = 1/4

30% = 0.3 = 3/1033.33% = 33.33/100 = 0.3333 = 1/3

37.5% = 0.375 = 3/840% = 0.4 = 2/5

50% = 0.5 = 1/260% = 0.6 = 3/5

62.5% = 0.625 = 5/866.66% = 66.66/100 = 2/3

75% = 0.75 = 3/480% = 0.8 = 4/5

87.5% = 0.875 = 7/8100% = 1

125% = 1.25 = 1 1/4

150% = 1.5 = 1 1/2200% = 2

Read


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T U E S D A Y , J U N E 1 1 , 2 01 3

Problems on Numbers with Solutions

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The basic problem with us is, we all are get used to the simple life. We want things

appear to be simpler. If we find the question like what will be the value of(2/3)*(1/5)*(3/7)*5, we just solve it in a fraction of seconds. But if we come across

the questions like what will be the two third of one fifth of three seventh of

five then we just skip to the next question. Where is problem? The problem is withour mindset. All of us keep on telling our minds that these questions are hard. But

trust me guys, these are very simple problems to solve. All that you have to do is,to just put your mind on the problem. Here, with this post we are giving you some

problems that appears to be harder at first glance but really very simple to solve.

These are very important for any competitive exam. All the best and Happy

Reading :)

1. If two third of one fifth of three seventh of a number is 4, what is the

number?

Solution :

Two Third of X is nothing but (2/5)X
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One Fifth of X is nothing but (1/5)X

Three Seventh of X is nothing but (3/7)X

So, here two third of one fifth of three seventh of a number is 4, that means

2. If three fifth of two seventh of a number is 24, what is its 40% ?Solution :
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here we need 40% cent of the number.

40 per cent means (40/10)th of the given number.

So, (40/100)*140 = 56is the required answer.

3. If three fourth of two third of a number is 12, what is the sum of its digits?Solution:

(3/4)*(2/3)*X = 12

So we get the number X = 24

the sum of its digits is 2+4 = 6

4. Two third of the first number is same as three fourth of the second number.

What is their ratio ?

Solution :Generally people tend to find out first and second numbers at first and later willfind out their ratios. But there is a simple technique to solve these type of

problems.

say First number is Fand the second number is S,

given that (2/3)*F = (3/4)*S

so, F/S = (3/4)*(3/2) = 9/8

what are you waiting for? the required ratio is 9:8 ;) simple.. isn't it?

5. Sum of two digits number and the number obtained by interchanging the

digits is 44. What is the sum of the digits of the number ?

Solution :

Assume that the two digits of the given number are Xand YGiven that,


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So, the sum of the two digit number and the number obtained by interchanging thedigits will be,

(10X+Y)+(10Y+X) = 44

=> 11X + 11Y = 44

so, X+Y = 4

6. Difference between a two digits number and the number obtained by

interchanging the digits is 36. What is the difference between the digits of the

number ?Solution :Same process as above,

(10X+Y) - ( 10Y+X) = 36

10X + Y - 10Y - X = 36

=> 9X - 9Y = 36

X - Y = 4 so required answer is 4
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7. Sum of a two digits number and the number obtained by interchanging the

digits is 55. Which of the following could be the difference between the digits

of the number ?1. 22.

3

3. 44. 75. 8

Solution :

10X + 10Y + X = 5511X + 11 Y = 55 => X+Y= 5

we know the sum of the two numbers (x+y) is 5 and we also know that the Sumof a two digits number and the number obtained by interchanging the digits is

55

So, now we should check combinations of X+Y=5 , the combinations shouldbe (1,4), (3,2)

Now we should check the second rule Sum of a two digits number and the

number obtained by interchanging the digits should be 55

According to this rule, we are getting numbers (32, 23), (14,41), (23, 32), (41, 14).Just check the given multiple choice options in the exam and choose the suitable

option.

According to the given options the answer should be 3. (The difference betweennumbers 1 and 4.

Some important points to keep in mind : The sum of a 2 digit number and the number obtained by interchanging thedigits is always divisible by 11. The differencebetween a two digit number and the number obtained byinterchanging the digits is always divisible by 9.

If the sum of a 2 digit number and the number obtained by interchanging thedigits of that number is given, the difference of the digits cannot be exactlyfound.


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If the difference of a 2 digit number and the number obtained byinterchanging the digits of that number is given, the sum of the digits cannot beexactly found.

8. Sum of the digits of a two digits number is 9. When the digits are

interchanged the number will be decreased by 9. What is the number?Solution:

Given that, X+Y = 9 --------------------(1)

and when the digits are interchanged, the number will be decreased by 9. That

means

(10X + Y) - (10Y+X) = 9

10X + Y - 10Y - X = 9

9X - 9Y = 9

=>X-Y = 1 --------------------(2)

So, 2X = 10

=> X = 5

from (1), Y will be 4.

So the number is 54

9. When 45 is added to a number, it will be increased by 20%. What is the

number ?Solution:

Then number is increased by 20%. That means the number is becoming 100% +20% = 120%

(X + 45) = (120/100) X

100X + 4500 - 120 X = 0


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=> X = 225

Shortcut Method :

if we add 45, the number is increasing 20%

then how much should we add to make it 100 %??

20% ------ 45

100% -------- ???

here we should multiply 20 with 5 to get 100. So just multiply 45 with the same 5.

So you will get 45 X 5 = 225

10. When 20 is subtracted from a number, it will be decreased by its 25%.

What is the number ?Solution :

same logic25% ----------- 20

100% ----------- ?

So, the answer is 20 X 4 = 80

That's all for now friends. In our next post we shall discuss some more typical

problems on Numbers with detailed explanations. And one more thing, for the

explanatory purpose we have clearly mentioned each and every step here. But its

advisable to all these calculations mentally without using pen and paper. Initiallyyou may find it little harder. But with practice you surely can do that. All the best

:)

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solutions.html#ixzz2ifWDl9cx

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M O N D A Y , M A Y 1 4 , 20 12

Finding the Square of the given Number

In this post we shall discuss about the Shortcut of finding the Square of the Given

Number. This is very easy and Simple method. All the you need to learn this

method is little concentration and little patience. Remember friends, To make you

understand the process clearly, we are posting the process in Step by Step process.But you have to do all these steps Mentally and you should Only write the Answer

on Paper...

Lets start with an example. Assume that you have to find the Square of the number38.

So, the general process is 382 multiplying 38 with itself. But this process take

much time and effort. So, instead of calculating 38 X 38, just use the formula a2+

2ab + b2

But here you should apply a little trick. If you apply the above formula as it is...

you cant get the answer... Just do as mentioned below.
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Now, follow the below mentioned steps
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Thats it... The answer is 1444.

Now lets have a look at another example. Lets see how to find out the square of 56.

I mean 562.

Now treat 6 as a, and 5 as b and apply the a2+ 2ab + b

2formula as explained

above.

First of all, find the a 2i.e., 6 2= 36.

Now find 2ab i.e., 2 X 6 X 5 = 60
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Now find the b 2 i.e., 5 2 = 25, now add this 25 to 6 = 31. And put thisbefore the numbers 3 6. So it will become 3 1 3 6

This is our answer 56 2= 3136Advantages of this Method :

We are dividing the given number into two small numbers and thenperforming calculations on those smaller numbers. So that you can do

calculations Mentally in very easy way. Initially you may think that this method is little confusing. Just do 3 or 4problems, so that you can find the advantage of this method.

If you have any Comments, please use the comments box below. Please tell your

friends about us if you like this Post.. Good Day and Happy Reading :)

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W E D N E SD A Y , M A Y 3 0 , 2 0 12

Shortcut for Square - A Simple Method

We have already discussed amethod for finding the squares of the given number

(check that methodHere). Now we shall discuss another simplest method tocalculate square of the given number. First of all one thing you should keep in
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mind, for you r convinience we've mentioned each and every step in detail.

But You should do all these calculations MENTALLY. I mean without using penor pencil. So practice well to do these problems orally. Now lets go to the

topic, Finding the square of a number ending in 5 is very simple. If the last digit of

the number is 5, then the last two digits of the square will be 25.What ever is theearlier part of the number multiply it with one more than itself and that will be the

first part of the answer. (The second part of the answer will be 25 only).

352 = 1225 Here 3 x 4 = 12 so the answer is 1225452 = 2025

552 = 3025

752 = 5625952 = 9025

1252 = 15625

1752

= 306252352 = 552251952 = 38025

2452 = 60025

Well friends, now we know the squares of numbers 25, 30, 35, 40, 45, 50, 55 etc. If

we want to find the squares of any other number, we find it using these squares

which we already know.

For 262 we will go from 252, for 322 we go from 302 and so on.

One way is writing 262= (25+1)2. But we need not even calculate (a+b)2by

adopting the following method.

262 = 252+ 26thodd number. i.e., 625 + 51 = 676

(a+b)2 = a2 + 2ab + b2

262 = (25 + 1 )2

= 252 + 2 x 25 x 1 + 12

= 625 + 50 + 1

= 625 + 51

= 676


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So, the answer is same. Now we shalllook at an easiest method which will help you to calculate Squares Mentally.

12 = 1 = 1

2 2 = 4 = 1+3

32 = 9 = 1+ 3 + 542 = 16 = 1 + 3 + 5 + 752 = 25 = 1 + 3 + 5 + 7 + 9

I mean, to get n2, you should add the FIRST n odd numbers. If we want 172, it will

be the sum of the FIRST 17 odd numbers.

nth

odd number is equal to (2n - 1)

Suppose you want to find out 6

2

knowing what 5

2

is, we can move from 5

2

to 6

2

.

62 will be the sum of 1st6 odd numbers. But the sum of the first 6 odd numbers canbe written as " Sum of the first 5 odd numbers" + "Sixth odd number". Since we

already know that the sum of the FIRST 5 odd numbers is 52, i.e., 25, we need toadd the sixth odd number, i mean (2x 6-1) = 11 to 25 to give us 62= 36.

Similarly

312 = 900 + 31st Odd number = 900 + 61 = 961362= 1225 + 36th odd number = 1225 + 71

= 1296 (remember that 352= 1225)412 = 1600 + 81 = 1681

462= 2025 + 91 = 2116

1262 = 15625 + 251 = 15876

1962 = 38025 + 391 = 384162162 = 46225 + 461 = 46656
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Read more: http://www.gr8ambitionz.com/2012/05/another-simple-method-for-

calculating.html#ixzz2iffMj6gV


Simple Method for Calculating Shortcut for Square - Part 2

We've already seen how to find the squares of numbers which are one more than

those whose squares we already know (eg 25, 30, 35 etc).Read that postHere.Similarly, we can find the squares of numbers which are one less than the numbers

whose squares are known already to us. For Example,292= 30 - 30th odd number = 900 - 59 = 841

392= 40 - 40th odd number = 1600 - 79 = 1521342= 1225 - 69 = 1156

542= 3025 - 109 = 2916742= 5625 - 149 = 5476

942= 9025 - 189 = 88362142= 46225 - 429 = 45796

So, we have seen how to get the squares of numbers which are one more or one

less than the numbers whose squares we already know (i.e., 25, 30, 35, 40, etc)

Now, we shall see how to get the squares of numbers which are 2 more or less thanthe numbers whose squares we already know.

272= 262+ 27th odd number = 252+ 26th odd number + 27th Odd number.

The sum of the 26th odd number and 27th odd number is the same as 4 times 26

So,

272 = 252+ 4x26 = 625 + 104 = 729572 = 3025 + 224 (4 times 56) = 3249

77 2 = 5625 + 304 (4 times 76) = 5929

972 = 9025 + 384 (4 times 96) = 9409

Similarly, we can find out the squares of numbers which are 2 less than thenumbers whose squares we know
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282 = ( 302 - 4 times 29) = 900 - 116 = 784532 = (552 - 4 times 54) = 3025 - 216 = 2809

932 = 9025 - 376 = 8649

2432= 60025 - 976 = 59049

Note : You should do all these calculations MENTALLY. I mean without usingpen or pencil. So practice well to do these problems orally.

Read more: http://www.gr8ambitionz.com/2012/05/another-simple-method-for-

calculating_30.html#ixzz2iffp3S2s



M O N D A Y , A U GU ST 1 9 , 2 0 13

How to find a Square Root - A Shortcut Method

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Friends, today we shall discuss the shortcut method for finding square roots. Lets

start this post with some basic definitions.

What is Square Root ?The square root of a number is any value when multiplied by itself, gives the

number. Pretty simpler definition. Isn't it?
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Now lets have a look at some examples3x3 = 9 so the square root of the number 9 is 36 x 6 = 36 so the square root of the number 36 is 6

we represent square roots with the" " symbol.(Trust me its a square rootsymbol. Not a tick mark :P )

well, now we have a good idea of what is a Square root and how it looks like. Nowlets come to our main topic.

How do you find Square Root ?

Well, its not such a complicated thing as you have been thinking. Trust me, After

reading this post you surely will be able to calculate square root of any number.

Before going to find the square root of any number, you should check whether the

given number is a square or not.

Check the units place (right most digit) of the given number. If you find2, 3,

7 and 8 at the unit place then we can say that the given number is not a squarenumber and you can't find square root for the given number.

Ex : 652 is not a square number because there is 2 at the unit place of the number.
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The perfect square always ends with the numbers 1, 4, 5, 6, 9and 0

(Update : this statement caused confusion to a number of our readers. This doesn'tmean all the numbers ending with the above mentioned values are square

numbers).

Now you have got a number to find its square root. Which is having one of these

numbers 1, 4, 5, 6, 9 at the end. Now check the below table. Just try to rememberit. Ofcourse, you easily can remember the values. Can't you ? :)

Units Place Factors

1 1 or 9

4 2 or 8

5 56 4 or 6

9 3 or 7

0 0

It simply says,if the given number has 1 at the unit's place, then its square root will have 1 or 9 at

the end (this is because 1x1 = 1 and 9 x 9 = 81)if the given number has 4 at the unit's place, then its square root will have2 or 8 at

the end (this ie because 2x2 = 4 and 8x8 = 64)You know the logic behind 5

for 6, you will have 4 or 6 (4x4 = 16 and 6x6 = 36)9, you will get 3 or 7 (3x3 = 9 and 7x7 = 49)

Ok, now come to the actual method of finding square roots of the given number.

Inorder to find the square root of the given number, you just should remember thefollowing manthra. Just mug-up the following four lines.

1. Nearest Square2. Its root -----------> this will be the first number of our squareroot.3. Its double4. Join the factor and multiply with it --------> the factor will be thesecond number of our square root


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Now lets see, how our table and manthra will help you finding square root of the

number.

Assume that you should find out the value of 2601

Given number is a square number (having 6 at the end). So we can find the squareroot of this number.

Step 1 : Take the Nearest Square of the first two digits of the number. Nearestsquare to the number 26 is 25 right?

Step 2 :Its root. (root of 25 is 5) -----------> First digit of our answer

Step 3 :Its double (double of 5 is 10)

now see, the below process,

Now, we have 101 at the reminder. You have nothing to do with the number. Just

consider the ending number. Which is 1. According to our above table the factorsof 1 are 1and 9.

Step 4 : Join the Factor and multiply with it. For this step always try the smallernumber, if it doesn't suits then only go with the larger number. Here in our case the

smaller number is 1. So join it to 10. So it will become 101. Now multiply it with1. We will get (101x1 = 101). So the second digit of the answer is 1.
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So required square root is 51.

Lets have a look at another example,

Find the square root of 4096.

4096

Step 1 : Take the Nearest Square of the first two digits of the number. Nearest

square to the number 40 is 36.

Step 2 :Its root. (root of 36 is 6) ------------>this is the first digit of our

required answer

Step 3 :Its double (double of 6 is 12)
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Now, we have 496 at the reminder. Consider the ending number. Which is 6.According to our above table the factors are 4or 6.

Step 4 : Join the Factor and multiply with it. Try the smaller number, which is4. Join it to 12 and it will becomes 124. Now multiply with the same number.

124x4 = 496. Which is our reminder.So the second number will be 4.

So, 64isthe square root of the given number.

Note : If you cant get the required reminder while joining the first number, then

simply join the second number. It will be your answer :)

Impor tant Note : To make every step clear to understand, we have used these

many steps. The process is very simple if you get the basic idea of it. So try to

reduce the steps while working with this method.

Read more: http://www.gr8ambitionz.com/2013/08/how-to-find-square-root-

shortcut-method.html#ixzz2ifgeDBQK

Under Creative Commons License: Attribution
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