Basic Mathematics for College Students

386 Chapter 4 Decimals

SECTION 4.6

Square Roots

Objectives

1 Find the square root of a

perfect square.

2 Find the square root of fractions

and decimals.

3 Evaluate expressions that

contain square roots.

4 Evaluate formulas involving

square roots.

5 Approximate square roots.

We have discussed the relationships between addition and subtraction and between

multiplication and division. In this section, we explore the relationship between

raising a number to a power and finding a root. Decimals play an important role in this

discussion.

1 Find the square root of a perfect square.

When we raise a number to the second power, we are squaring it, or finding its square.

The square of 6 is 36, because.

The square of is 36, because.

The square rootof a given number is a number whose square is the given number. For

example, the square roots of 36 are 6 and , because either number, when squared,

is 36.

Every positive number has two square roots. The number 0 has only one square

root. In fact, it is its own square root, because 02  0.

 6

 6 (6)^2  36

62  36

Square Root

A number is asquare rootof a second number if the square of the first

number equals the second number.

EXAMPLE (^1) Find the two square roots of 49.
StrategyWe will ask “What positive number and what negative number, when
squared, is 49?”
WHYThe square root of 49 is a number whose square is 49.
Solution
7 is a square root of 49 because
and
 7 is a square root of 49 because (7)^2  49.

72  49

Self Check 1

Find the two square roots

of 64.

Now TryProblem 21

In Example 1, we saw that 49 has two square roots—one positive and one

negative. The symbol is called a radical symboland is used to indicate a positive

square root of a nonnegative number. When reading this symbol, we usually drop the

word positiveand simply say square root.Since 7 is the positive square root of 49, we

can write

represents the positive number whose square is 49.

Read as “the square root of 49 is 7.”

When a number, called the radicand,is written under a radical symbol, we have a

radical expression.

Radical symbol

149  Radicand

149  7 149

1

Radical expression

b