Beginning Algebra, 11th Edition

Finding Square Roots

Find each square root.

(a)

The radical represents the positive or principal square root of 144. Think

of a positive number whose square is 144.

so

(b)

This symbol represents the negative square root of 1024. A calculator with a

square root key can be used to find Therefore,

(c) (d) (e) NOW TRY

As shown in the preceding definition, when the square root of a positive real

number is squared, the result is that positive real number. AAlso, A 20 B

2

=0.B

- 2 0.81=0.9

B

16

49

=-

4

B^7

4

9

=

2

3

- 21024 = -32.

21024 =32.

- 21024

122 =144, 2144 =12.

2144

2144

EXAMPLE 2

SECTION 8.1 Evaluating Roots 495

Square Roots of a

If ais a positive real number, then

is the positive or principal square root of a,

and is the negative square root of a.

For nonnegative a,

and

Also, 20 =0.

 2 a# A 2 aBA 2 aB

2

2 a# 2 aA 2 aB a.

2

a

 2 a

2 a

We summarize our discussion of square roots as follows.

NOW TRY
EXERCISE 2
Find each square root.

(a) (b)

(c)
B

100

121

2400 - 2169

NOW TRY
EXERCISE 3
Find the square of each
radical expression.

(a) (b)

(c) 22 k^2 + 5

215 - 223

NOW TRY ANSWERS

2. (a) 20 (b) (c)


3. (a) 15 (b) 23 (c) 2 k^2 + 5

10

• (^1311)
  Squaring Radical Expressions
  Find the squareof each radical expression.
  (a)
  Definition of square root
  (b)
  The square of a negativenumber is positive.
  (c)
  A^2 p^2 +^1 B NOW TRY
  2
  =p^2 + 1
  2 p^2 + 1

A- 229 B

2

= 29

- 229

A^213 B

(^2) = 13

213

EXAMPLE 3