Algebra 1 Common Core Student Edition, Grade 8-9

Simplifying Radicals

Co m m o n Co r e St a t e St a n d a r d s

Prepares for A-REI.A.2 Solve sim ple rational and

radical equations in one variable, and give examples

showing how extraneous solutions may arise.

MP 1, MP 2, MP 3. MP 4, MP 7

Object ive To simplify radicals involving products and quotients

Get t i n g Read y!

Use what you know

about triangles to

solve th is problem.

MATHEMATICAL

PRACTICES

Suppose you are bringing a

mirror into your living room.

W h a t is t h e m a x im u m h e ig h t

of a square mirror that will fit

through th e doorway shown?

Justify your reasoning.

Lesso n t

Vocabulary

• radical ex p ressio n


• ra tio n a lize th e
  denom inator

In the Solve It, the maximum height of the mirror is a radical expression. A

radical expression, such as 2 V 3 or V x + 3, is an expression that contains a radical.

A radical expression is simplified if the following statements are true.

• The radicand has no perfect-square factors other than 1.


• T h e r a d i c a n d c o n t a i n s n o f r a c t i o n s.


• No radicals appear in the denominator of a fraction.

Simplified

3 V 5 9 V x V2 4

Not Simplified

3VI2^5

V7

Esse n t i a l U n d e r st a n d i n g You can simplify radical expressions using

multiplication and division properties of square roots.

Pr o p er t y Multiplication Property of Square Roots

Algebra Example

For a a 0 and b s 0, \/ab = Va • Vh. V48= V16 • V3 = 4V3

V J

You can use the Multiplication Property of Square Roots to simplify radicals by

removing perfect-square factors from the radicand.

' I Lasson 10-2 Simplifying Radical, ' 6 1 9