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6.1 & 6.2 Rational Exponents and Radicals

Total questions: 10

Worksheet time: 15mins

Name
Class
Date
1.

Find the indicated real nth root(s) of a.

n = 5 , a = -243

a)

3

b)

-3

c)

±3

d)

no real roots

2.

Find the indicated real nth root(s) of a.

n = 8 , a = 256

a)

2

b)

-2

c)

±2

d)

no real roots

3.

Find the real solution(s) of 5x3 = 320.

a)

4

b)

±4

c)

8

d)

±8

4.

Find the real solution(s) of (x + 3)4 = 24.

a)

x ≈ 2.14

b)

x ≈ 2.14 or x ≈ -2.14

c)

x ≈ - 0.79 or x ≈ -5.21

d)

x ≈ - 0.79

5.

Find the radius, given V = 4/3 π r3

a)

7.18 ft

b)

6.00 ft

c)

4.51 ft

d)

3.72 ft

6.

An expression containing a radical with index n is in simplest form when these three conditions are met.

a)

No radicands have perfect nth powers as factors.

b)

No radicands contain negative numbers.

c)

No radicands contain fractions.

d)

No radicals appear in the numerator of a fraction.

e)

No radicals appear in the denominator of a fraction.

7.

Write in simplest form. ∛500

a)

167 ⅔

b)

5 ∛4

c)

10 √5

d)

3 ∛167

8.

Identify the conjugate of a√b + c√d

a)

a√b + c√d

b)

a√b - c√d

c)

√b - √d

d)

√b + √d

9.

To rationalize a denominator of 2 - √7

a)

multiply the numerator and denominator by √7

b)

multiply the denominator by 2 + √7

c)

multiply the numerator and denominator by 2 - √7

d)

multiply the numerator and denominator by 2 + √7

e)

multiply the denominator by √7

10.

Simplify ∛(27d12)

a)

9d4

b)

3d4

c)

3d9

d)

9d9