n th Root & Rational Exponents

nnthth Root & Root &Rational Exponents Rational Exponents

3.13.1

Square RootSquare Root Cube root

Cube root

44thth Root Root nn thth Root

Root

y xRadicandRadicand

IndexIndex

Square RootSquare Root

Cube root

Cube root

44thth Root Root

25 5 5 5 25because

3 8 2 2 2 2 8because

4 16 2 2 2 2 2 16because

4 81 3 because __________________

Writing expressions with Writing expressions with nnthth Roots vs. Rational Roots vs. Rational

ExponentsExponentsRadical ExpressionRadical Expression Exponential ExpressionExponential Expression

3

15

23

25

1. 125

2. 32

3. 8

4. 32

Radical ExpressionRadical Expression Exponential ExpressionExponential Expression

23

4

1. 27

2. 923

52

3. 125

4. 4

PowerRoot

base

Cube rootCube root 3 x Same as Same as 13x

Can x be negative?Can x be negative?When?When?

3 8

4 16

3 8

4 16

Number of Solutions to ConsiderNumber of Solutions to Consider

Negative ExponentsNegative Exponents 24 2

14

116

2327 2

3

1

27 2

3

1

27 2

13

19

2532

Evaluate the expression using a calculator. Evaluate the expression using a calculator. Round the results to the 100Round the results to the 100thsths when when appropriate.appropriate.

13

15

25

1. 14

2. 36

3. 16

2 3

4

1. 6 180 2. 9 31

3. 8 2

x x

x

The volume of a The volume of a beach ball can be beach ball can be approximated using approximated using the model the model where r is the radius where r is the radius of the ball in inches. of the ball in inches. Estimate the radius of Estimate the radius of the ball if the volume the ball if the volume is 268 cubic inches.is 268 cubic inches.

343

V r

343

V r

342683r

HOMEWORK: HOMEWORK: Page 112 #1–35 odd,Page 112 #1–35 odd,