Easy Algebra Step-by-Step

Roots and Radicals 33

A number that is an exact square of another number is a perfect square.

For instance, the integers 4, 9, 16, and 25 are perfect squares. Here is a help-

ful list of principal square roots of some perfect squares.

00 , 11 , 42 , 93 , 16 =^4 ,

25 = (^5) , 36 = 6 , 49 = 7 ,
64 = 8 , 81 = 9 , 100 = 10 , 121 = 11 ,
144 = 12 , 169 = 13 , 196 = 14 ,
225 = 15 , 256 = 16 , 289 = 17 ,
400 = 20 , 625 = 25
Also, fractions and decimals can be perfect squares. For instance,

9

25

is a

perfect square because

9

25

equals

3

5

3

5

⋅ , and 0.36 is a perfect square because

0.36 equals (.. 6 )( 0 .).. If a number is not a perfect square, you can indicate its

square roots by using the square root symbol. For instance, the two square roots

of 15 are 15 and − 15.

Problem Find the two square roots of the given number.

a. 25

b.^4

9

c. 049

d. 11

Solution

a. 25

Step 1. Find the principal square root of 25.

555 = 25 , so 5 is the principal square root of 25.

Step 2. Write the two square roots of 25.

5 and − 5 are the two square roots of 25.

Working with square roots will be

much easier for you if you memorize

the list of square roots. Make

fl ashcards to help you do this.