Algebra 1 Common Core Student Edition, Grade 8-9

Object ive To rewrite expressions involving radicals and rational exponents

Get t i n g Read y!

Make a sketch

and look f o r right

triangles. Look

for a pattern in

your answers and

predict t he value

of c before finding

the value of c.

Th e f ig u re at t h e r ig h t is made up o f

sq u ar es. Th e sid e o f a l ar g er sq uare is

bisect ed by t he vert ices o f t he square

t h at is one size sm aller. W hat are

t he values o f a, b , and c? (Hin t : The

hypotenuse of an isosceles rig ht triangle

equals a sm aller sid e t im es V2.)

MATHEMATICAL

PRACTI CES

Lesso n
Vocabulary
index

In this lesson, you will learn the relationship between radical expressions and

expressions using rational exponents.

Esse n t i a l U n d e r st a n d i n g You can use rational exponents to represent radicals.

In a radical expression, the number under the radical sign a is the radicand.

The number n in the crook of the radical sign is the index. The index gives

the degree of the root. For a cube root, the degree is 3. If there is no index, the

degree is 2 , which means square root.

Recall what you know about square roots. Since 5 2 = 25, you know that

V25 = 5. You also know that 25^ = 5. Using the transitive property of

equality, you can conclude that V25 = 252. Similarly, Y;8 = 8 T

radical sign

radicand

Rat i o n al Exp o n en t s

and Rad icals

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

N-RN.A.2 Rewrite expressions involving radicals and

rational exponents using the properties o f exponents.

MP 1, MP 3, MP 4, MP 6, MP 7

You can simplify radical expressions by finding like factors, just as when

simplifying powers with rational exponents.

How do you find V a

for any number a?

Yo u l o o k f o r n equal

factors of a.

Fi n d i n g Ro o t s

What is the simplified form of each expression?

0 \Zl25 0 ^ 1 6

Method 1 Method 2

N/i25 = ^5*5*5 \/l6=16?

= 5 =(2*2

= 2

2 • 2)5

Ch ap t e r 7 Ex p o n e n t s a n d Ex p o n e n t i a l Fu n c t i o n s