11.2A

Simplify and Multiply Square Roots

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 9

Notice squaring any number always results in a ___________________ number. positive

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

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

9

1

232

m2

25

3 1

23 m

Not possible!

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

m2 –m

–x

x22y3

Factor tree inside radical

Circle any pairs

Multiply pairs w/ # in front

Multiply loners back inside

Ex 4: Simplify

a) 20

5 4

2 2

= 2 5

2 36

6 6

72

23 23

b)= 6 2

Ex 4: Simplify

c) 250x

2 25

5 5

x x

= 5 2x

Ex 4: Simplify

d) 624x

2 12

2 6

2 3

x x x x x x

= 2 6x3

Ex 4: Simplify

e) 22 18x

2 9

3 3

x x

= 6 2x

Ex 4: Simplify

f) 165 12y

3 4

2 2

= 10 3y8

10 10

107 100x =

g)

70x5

h)

5 8

4 2

83 40y

2 2

= 6 10y4

Multiply #s in front

Multiply #s inside

Factor tree and simplify

2 35

5 49

7 7

= 35

20x2

5 4

2 2

= 2 5x

240y10

24 10

6 4

3 2 2 2

2 5

= 4 15y5

6 5t6 = 6 5t3

14 12k8

4 3

2 2

= 28 3k4

Divide exponent by 2

Leave remainder 1 inside

x x x

= xx

= 4 pp2

6 4

3 2 2 2

= 2 6kk9

8 4

4 2

2 2

22

= 20 2ww7

6 6

= 6 pp3

7 4

2 2

= 2 7xx7

63y5

9 7

3 3

= 3 7yy2

80d5

8 10

4 2

2 2

2 5

= 4 5dd2

150x7

15 10

3 5 5 2

= 5 6xx3

243x13

27 9

9 3

3 3

33

= 9 3xx6