Beginning Algebra, 11th Edition

494 CHAPTER 8 Roots and Radicals

OBJECTIVES OBJECTIVE 1 Find square roots.In Section 1.2,we discussed the idea of the

squareof a number. Recall that squaring a number means multiplying the number by

itself.

The square of 7 is 49.

The opposite (inverse) of squaring a number is taking its square root. This is equiva-

lent to asking

“What number when multiplied by itself equals 49?”

From the example above, one answer is 7, since

This discussion can be generalized.

7 # 7 =49.

72 = 7 # 7 = 49

Evaluating Roots

8.1

1 Find square roots.

2 Decide whether a

given root is

rational, irrational,

or not a real

number.

3 Find decimal

approximations for

irrational square

roots.

4 Use the

Pythagorean

theorem.

5 Use the distance

formula.

6 Find cube, fourth,

and other roots.

Square Root

A number bis a square rootof aif b^2 a.

NOW TRY
EXERCISE 1
Find all square roots of 81.

Finding All Square Roots of a Number

Find all square roots of 49.

We ask, “What number when multiplied by itself equals 49?” As mentioned

above, one square root is 7, because Another square root of 49 is ,

because

Thus, the number 49 has twosquare roots: 7 and. One square root is positive, and

one is negative.

- 7

1 - 721 - 72 =49.

7 # 7 =49. - 7

EXAMPLE 1

NOW TRY

The positiveor principal square rootof a number is written with the symbol

For example, the positive square root of 121 is 11.

The symbol is used for the negative square rootof a number. For example,

the negative square root of 121 is.

The symbol , called a radical symbol,always represents the positive square

root except that The number inside the radical symbol is called the

radicand,and the entire expression — radical symbol and radicand — is called a radical.

Radical symbol Radicand

Radical

An algebraic expression containing a radical is called a radical expression.

The radical symbol has been used since 16th-century Germany and was

probably derived from the letter R. The radical symbol in the margin comes from the

Latin word radix,for root. It was first used by Leonardo of Pisa (Fibonacci) in 1220.

2

2 a

A^20 =^0 B.

2

- 2121 =- 11

- 11

- 2

2121 = 11

2.

NOW TRY ANSWER
1.9, - 9

Early radical symbol

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