Free Printable Topic 5 Review: Rationale Exponents and Radical Functions

1.

In the expression $^n\sqrt{c}$ , n is the _______.

a)

extraneous solution

b)

index

c)

$n^{th}$ root

d)

radicand

2.

In the expression $^n\sqrt{c}$ , c is the _______.

a)

extraneous solution

b)

index

c)

$n^{th}$ root

d)

radicand

3.

Radicals with the same index and the same radicand are _________.

a)

composite functions

b)

inverse functions

c)

like radicals

d)

reduced radical form

4.

A(n) _________ is a function defined by a radical expression

a)

Composite function

b)

Inverse function

c)

Radical function

5.

A(n) __________ of a number c is x, such that $x^n=c$ .

a)

extraneous solution

b)

$n^{th}$ root

c)

radicand

d)

reduced radical form

6.

A(n) __________ is a potential solution that must be rejected because it does not satisfy the original equation.

a)

extraneous solution

b)

$n^{th}$ root

c)

radicand

d)

reduced radical form

7.

When all $n^{th}$ roots of perfect $n^{th}$ powers have been simplified and no radicals remain in the denominator, an expression is in ________________.

a)

like radicals

b)

composite functions

c)

reduced radical form

8.

A(n) _____________ results from the application of one function to the output of another function.

a)

composite function

b)

inverse function

c)

radical function

9.

Rewrite the expression using a fractional exponent: $\ ^4\sqrt{16^2}$

a)

$16^{\frac{2}{4}}$

b)

$16^{\frac{4}{2}}$

c)

4

d)

256

10.

What is the value of the expression? $-^3\sqrt{125^5}$

a)

3125

b)

-3125

c)

18.12

d)

-18.12

11.

Simplify. $^3\sqrt{\left(-2z^2\right)^3}$

(a)

12.

What is/are the real fourth root of 81?

a)

3

b)

9

c)

20.25

d)

-3

e)

-9

13.

Simplify: $^3\sqrt{8y^9}$

a)

$2y^3$

b)

$\frac{8}{3}y^3$

c)

$2\sqrt{2}y^{\frac{9}{2}}$

d)

$2y^6$

14.

Simplify: $^6\sqrt{729a^{24}b^{18}}$

a)

$121.5a^{18}b^{12}$

b)

$27a^{12}b^9$

c)

$3a^4b^3$

15.

Solve: $1125=9x^3$

a)

5

b)

25

c)

-5

d)

-25

16.

Solve: $6480=5w^4$

a)

6

b)

36

c)

324

d)

-6

e)

-36

17.

Simplify: $\left(3x^{\frac{1}{2}}\right)\left(4x^{\frac{2}{3}}\right)$

a)

$7x^{\frac{7}{6}}$

b)

$12x^{\frac{1}{3}}$

c)

$12x^{\frac{7}{6}}$

d)

$7x^{\frac{1}{3}}$

18.

$\sqrt{3x^6y^4}\cdot\sqrt{3x^8y^6}$

a)

$9x^{24}y^{12}$

b)

$3x^{24}y^{12}$

c)

$9x^{14}y^{10}$

d)

$3x^7y^5$

19.

$^3\sqrt{\frac{250f^7g}{2f^2g^3}}$

a)

$5f^{\frac{5}{3}}g^{\frac{1}{6}}$

b)

$5f^{\frac{5}{3}}g^{\frac{2}{3}}$

c)

$25f^{\frac{5}{2}}g^{\frac{1}{4}}$

d)

$25f^{\frac{5}{2}}g$

20.

Add or subtract: $2\cdot^3\sqrt{5}+2\sqrt{5}-7\sqrt{5}$

a)

$-3\cdot^3\sqrt{5}$

b)

$-3\sqrt{5}$

c)

$2\cdot^3\sqrt{5}-5\sqrt{5}$

21.

Multiply: $\left(9\sqrt{x}+9\right)\left(5\sqrt{x}+5\right)$

a)

$45x+90\sqrt{x}+45$

b)

$45x+45$

c)

$14\sqrt{x}+14$

d)

$45x^2+45$

22.

Solve. $^3\sqrt{12x}=-3$

(a)

23.

Solve. $\sqrt{2x-1}=3$

(a)

24.

Solve. $\sqrt{44-5x}=x-4$ . Use a comma to separate answers as needed. You do not need to include "x=" in your answer.

(a)

25.

Solve. $\left(x^2-x-51\right)^{\frac{3}{4}}-9=18$ . Use a comma to separate answers as needed. You do not need to include "x=" in your answer.

(a)

26.

Graph the function. $f\left(x\right)=\sqrt{x}-2$

a)

b)

c)

d)

27.

Write the function of the graph as y=

(a)

Topic 5 Review: Rationale Exponents and Radical Functions

Total questions: 27

Worksheet time: 17mins

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