squaring made easy

8/8/2019 Squaring Made Easy

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Squaring Made Easy (But First, learn by heart squares of numbers till 30):

Lets start with 50 to 60 numbers:

5 1 +1 (51= 50 + 1, so separate +1 as shown & multiply)

5 1 +1

26 01 = 2601 (Ans) (26 is obtained as 5*5 +1= 26)

So, 512

= 2601

Quickly,

5 2 +2

5 2 +2

27 04 = 2704 So, 522= 2704 (27 is obtained as 5*5 +2= 27)

So now all can be done mentally as:

532

= 28 09

542= 29 16

552= 30 25

562= 31 36

572= 32 49

582

= 33 64

592= 34 81

602= 3600

So, number 25 played a very important role here as we added units place of each number

above to 25 so as to obtain first two leftmost numbers.


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Now, lets do squaring of 50 to 60 numbers:

6 1 +11 (Here writing 61 as 50 + 11, so separated +11 as shown)

6 1 +11

36 121 = 37 21 ( First Multiplying 11*11=121, carrying 1 as shown; 36 is obtained as

applying the same logic as in 50-60 squares weve done, 25 +11=36; After adding, carry 1 in 36

we get 37)

So, if you understood the logic of squaring of 50 to 60, youd have understood this too.

Quickly,

6 2 +12

6 2 +12

37 144 = 38 44 (25+12=37, then +1 = 38)


632= 39 69

642= 40 96

652= 42 25

662= 43 56

672= 44 89

682= 46 24

692= 47 61

702= 4900


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Now for 40 to 50, applying the same logic

4 1 -9 (41= 50-9, so writing -9 separately)

4 1 -9

16 81= 1681 (9*9=81; 25-9=16)

Quickly again,

4 2 -8

4 2 -8

17 64=1764 (25-8= 17)


432= 18 49

442= 19 36

452= 20 25

462= 21 16

472= 22 09

482

= 23 04

492= 24 01

502=2500


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Now Squaring 30 to 40:

3 1 -19 (31= 50-19, so writing -19 separately)

3 1 -19

6 361= 961 (25-19=6; then add carry 3, we get 9)

Quickly,

3 2 -18

3 2 -18

7 324= 1024 (25-18=7, then add carry 3, we get 10)


332= 10 89

342= 11 56

352= 12 25

362

= 12 96

372= 13 69

382= 14 44

392= 15 21

402=1600

So, logic is simple, its just that how you use it frequently during practicing of questions.

Regards,

Ish Kumar Tripathi

squaring made easy

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