Beginning Algebra, 11th Edition

8.1

square root
principal square root
negative square root
radicand
radical
radical expression

perfect square

cube root

fourth root

index (order)

perfect cube

perfect fourth

power

8.3

like radicals

unlike radicals

8.4

rationalizing the

denominator

8.5

conjugate

8.6

radical equation

squaring property of equality

extraneous solution

KEY TERMS

2 radical symbol is approximately

equal to

« cube root of a

2 na nth root of a

23 a a1/n nth root of a

NEW SYMBOLS

1.Thesquare rootof a number is
A.the number raised to the second
power
B.the number under a radical sign
C.a number that, when multiplied by
itself, gives the original number
D.the inverse of the number.

2.Aradicalis
A.a symbol that indicates the nth
root
B.an algebraic expression
containing a square root
C.the positive nth root of a number
D.a radical sign and the number or
expression under it.

3.Theprincipal rootof a positive

number with even index nis

A.the positive nth root of the

number

B.the negative nth root of the

number

C.the square root of the number

D.the cube root of the number.

4. Like radicalsare
   A.radicals in simplest form
   B.algebraic expressions containing
   radicals
   C.multiples of the same root of the
   same number
   D.radicals with the same index.
   5. Rationalizing the denominatoris
   the process of
   A.eliminating fractions from a
   radical expression
   B.changing the denominator of a
   fraction from a radical to a
   rational number
   C.clearing a radical expression of
   radicals
   D.multiplying radical expressions.
   6.Theconjugateof is
   A.
   B.
   C.
   D. 1 a+b 22.

a,b

a#b

a-b

a+b

TEST YOUR WORD POWER

See how well you have learned the vocabulary in this chapter.

ANSWERS

SUMMARY

CHAPTER 8

1.C;Examples:6 is a square root of 36, since is also a square root of 36. 2.D;Examples:
3.A;Examples: 4.C;Examples: and are like radicals, as are and 5.B;Example:

To rationalize the denominator of , multiply numerator and denominator by to get. 6.A;Example:The conjugate of

23 + 1 is 23 - 1.

5 A 23 - 1 B

23 - (^12)
5
23 + 1
236 =6, 2481 =3, 2664 = 2 27 327 2236 k 5236 k.

62 = 6 # 6 =36.- 6 2144 , 24 xy^2 , 24 +t^2

544 CHAPTER 8 Roots and Radicals

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