Algebra 1 Common Core Student Edition, Grade 8-9

Which method should
yo u use?
If the denominator is
a p e rfe ct square, apply
the Division Property o f
Square Roots first. If not,
simplify the fraction first.

Does m ultiplying■. V7
an expression by
change its value?
No. The fra c tio n / = is
equal to 1. M u ltip ly in g
an expression by 1 won't
change its value.

Si m p l i f y i n g Fr act i o n s W i t h i n Ra d i c a l s

What is the simplified form of each radical expression?

Q

0

V&4

V49

8

7

Use the Division Property o f Square Roots.

Simplify V 6 4 and V 49.

/§Z

50x

/ 8x3.

50x V 25

V4x^

V25

v±____

V 25

2x

5

Divide the numerator and denominator by 2x.

Use th e D ivision Property o f Square Roots.

Use the M u ltip lic a tio n Property o f Square Roots.

Simplify V 4 , V? , and V 25.

£ Got It? 5. What is the simplified form of each radical expression?

a. '144 9 b. 36a4a3 C. 25/

When a radicand in a denominator is not a perfect square, you may need to rationalize

the denom inator to remove the radical. To do this, multiply the numerator and

denominator by the same radical expression. Choose an expression that makes the

radicand in the denominator a perfect square. It may be helpful to start by simplifying

the original radical in the denominator.

Rat i o n al i zi n g D en o m i n at o r s

What is the simplified form of each expression?

V3

Q V 7

V3 = V 3. V7

V7 V7 V7

= V2l

V49

V2l

0

Multiply by

V7

Vsn

V7 V7

V8n 2 V 2 n

V7 V2n

Multiply byV2V2n'n^

2 V2n V2n

Vlin

2V4~r?

= Vl4n

4n

Go t I t? 6. What is the simplified form of each radical expression?

V2 b V5

V3 ‘ Vl8m

a. c. \ / -If7s

622 Chapter 10 Radical Expressions and Equations