11.2a

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11.2A Simplify and Multiply Square Roots

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11.2A. Simplify and Multiply Square Roots. Squaring a Number . When a number is squared, it is multiplied to itself: . 1. 5. 5. 25. -3. -3. 9. Notice squaring any number always results in a ___________________ number. . positive. Taking the Square Root of a Number - PowerPoint PPT Presentation

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Page 1: 11.2A

11.2A

Simplify and Multiply Square Roots

Page 2: 11.2A

Squaring a Number When a number is squared, it is multiplied to itself:

21 1 1 __ 25 __ __ ___

2( 3) __ __ ___

1 5 5 25

-3 -3 9Notice squaring any number always results in a ___________________ number. positive

Page 3: 11.2A

Taking the Square Root of a Number

Just as subtracting is the opposite of

adding and dividing is the opposite of

multiplying, the opposite of squaring is

____________ ______________.square rooting

Page 4: 11.2A

Ex 1: Find the square roots of the following numbers:

9

1

232

m2

25

3 1

23 m

Not possible!

Page 5: 11.2A

Ex 2: Find the following: (Think of the negative sign in front as just being negative one multiplied to the positive root.)

232

25 –5

–23

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m2 –m

–x

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x22y3

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Factor tree inside radicalCircle any pairsMultiply pairs w/ # in frontMultiply loners back inside

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Ex 4: Simplify

a) 205 4

2 2

= 2 5

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2 36

6 6

72

23 23

b)= 6 2

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Ex 4: Simplify

c) 250x2 25

5 5

x x

= 5 2x

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Ex 4: Simplify

d) 624x2 12

2 6

2 3

x x x x x x

= 2 6x3

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Ex 4: Simplify

e) 22 18x

2 9

3 3

x x

= 6 2x

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Ex 4: Simplify

f) 165 12y

3 4

2 2

= 10 3y8

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10 10

107 100x =g)

70x5

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h)

5 8

4 2

83 40y

2 2

= 6 10y4

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Multiply #s in frontMultiply #s insideFactor tree and simplify

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2 35

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5 49

7 7

= 35

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20x2

5 4

2 2

= 2 5x

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240y10

24 10

6 4

3 2 2 22 5

= 4 15y5

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6 5t6 = 6 5t3

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14 12k8

4 3

2 2

= 28 3k4

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Divide exponent by 2Leave remainder 1 inside

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x x x

= xx

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= 4 pp2

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6 4

3 2 2 2

= 2 6kk9

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8 4

4 22 2

22

= 20 2ww7

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6 6

= 6 pp3

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7 42 2

= 2 7xx7

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63y5

9 73 3

= 3 7yy2

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80d5

8 104 2

2 22 5

= 4 5dd2

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150x7

15 10

3 5 5 2

= 5 6xx3

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243x13

27 9

9 3

3 3

33

= 9 3xx6