Intermediate Algebra (11th edition)

8.1

radicand
index (order)
radical
principal root
radical expression
square root function
cube root function

8.3

simplified radical

8.5

rationalizing the

denominator

conjugates

8.6

radical equation

extraneous solution

8.7

complex number

real part

imaginary part

pure imaginary number

standard form

complex conjugates

KEY TERMS

radical symbol

radical; principal nth

root of a

n

2 a

2 “positive or negative”

or “plus or minus”

is approximately equal

to

«



ato the power

ato the power

m

n

am/n

1

n

a1/n

i imaginary unit

NEW SYMBOLS

1.Aradicandis
A.the index of a radical
B.the number or expression under
the radical sign
C.the positive root of a number
D.the radical sign.

2.ThePythagorean theoremstates
that, in a right triangle,
A.the sum of the measures of the
angles is 180°
B.the sum of the lengths of the two
shorter sides equals the length of
the longest side
C.the longest side is opposite the
right angle
D.the square of the length of the
longest side equals the sum of
the squares of the lengths of the
two shorter sides.

3.Ahypotenuseis

A.either of the two shorter sides of

a triangle

B.the shortest side of a triangle

C.the side opposite the right angle

in a triangle

D.the longest side in any triangle.

4. 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.

5.Anextraneous solutionis a

solution

A.that does not satisfy the original

equation

B.that makes an equation true

C.that makes an expression equal 0

D.that checks in the original

equation.

6.Acomplex numberis

A.a real number that includes a

complex fraction

B.a zero multiple of i

C.a number of the form

where aandbare real numbers

D.the square root of -1.

a+bi,

TEST YOUR WORD POWER

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

ANSWERS

SUMMARY

CHAPTER 8

1.B;Example:In 3xyis the radicand. 2.D;Example:In a right triangle where and
3.C;Example:In a right triangle where the sides measure 9, 12, and 15 units, the hypotenuse is the side opposite the right angle, with measure

15 units. 4.B;Example:To rationalize the denominator of , multiply both the numerator and denominator by to get.

5.A;Example:The proposed solution 2 is extraneous in 25 x- 1 + 3 =0. 6.C;Examples:- 51 or- 5 + 0 i 2 , 7i 1 or 0+ 7 i 2 , 2 - 4 i

5 A 23 - 1 B

23 - (^12)
5
23 + 1
23 xy, a=6,b=8, c=10, 62 + 82 = 102.

CHAPTER 8 Summary 483