High School Common Core

Number & QuantityThe Real Number System – Use properties of

rational and irrational numbers.

Multiply & Divide Radicals

Name Date

Subject Period

Radical Property (Multiplication)

You can multiply numbers if they are both INSIDE the radicals.

a = a bb = ab

3 = 3 22 = 6

-4 12

Ex1:

Multiply numbers on the OUTSIDE of the radical.

ExplainSimplify

Multiply numbers on the INSIDE of the radical.

Simplify Radical

2 5

-8

-8

60

4 15

-8 2 15

-16 15

Simplify -3 5-3 15

9

9

75

25 3

9 5 3

45 3

Simplify 6 32 – 2

-6

-6

64

8

-48

Simplify 3 6 8

3

3

48

16 3

3 4 3

12 3

Simplify -5 7 -4 3

20 21

Simplify 5 6-2 3

-10

-10

18

9 2

-10 3 2

-30 2

Simplify 5 7 20

7

7

100

10

70

Radical Property (Division)

You can divide numbers if they are both INSIDE the radicals.

a=

b

a

b

15=

5

15

5= 3

Ex2:

Divide numbers INSIDE radicals.

ExplainSimplify

Simplify Radicals

15 ÷ 5÷ 5

6

Divide numbers OUTSIDE radicals.

20

6 34

6 3 2

3 3

Simplify 10 ÷ 2÷ 2

232

2 516

2 5 4

1 5

2÷2÷

2

Simplify 27 ÷ 9÷ 9 9

3 1

3

Simplify 32 -52

-5 162

-5 2

-20 2 2

2

4 2

-10 2

Simplify 12 3

6

1

2

4

÷ 3÷ 3 6

6

2÷2÷

1 3

Simplify 24 3

4

1

2

8

2 2

÷ 3÷ 3

Simplify 64 4

84

8 20

5

25

4 ÷4 ÷

2 5