11-2Radical Expressions

Standard 2.0Three Key Terms

One Rule

CA Standard 2.0

Understand and use the operation of a taking a root.

Vocabulary Radical

Expression

Radicand

The entire expression written with a radical sign.

The expression that is written under the radical

42 x Radical Expression

Radicand

Vocabulary Imaginary

Number

A number that is not part of the real number system

Examples of Real and Imaginary Numbers

1.

2.

3.

4.

1. Irrational

2. Imaginary

3. Imaginary

4. Rational

37

5

65

100

#5 Evaluate the expression

8for 215 xx

)8(215

1615

1Imaginary

#6 Evaluate the expression

10for 48 yy

)10(48

408

32

Imaginary

#7 Real Number Sets Determine the values of x that make

each expression a real number.

1x

01x1x

#8 Real Number Sets Determine the values of x that make

each expression a real number.

32 x

032 x

2

3x

32 x

Perfect Square Radicands

The radical sign actually means the radicand is to the one-half power.

21

22 xx )2( 2

1x1x

x

Perfect Square Radicands

? Does 2 xx Partially

,3Then .3 Suppose 22 xx .3or 9 iswhich

,)3(Then .3 Suppose 22 xx .3or 9 iswhich

xx 2 So

#9 Simplify

2)(xy

21

2)(xy

xy

#10 Simplify

22 yx

21

22 yx

xy

#11 Simplify

2)1(x

21

21x

1x

#12 Simplify

1682 xx

2)4(x

21

2)4(x

4x

#13 Simplify

225y

21

25 y

y5

25 y