Free Printable G8 Simplifying radicals and radical functions

1.

What is the largest perfect square that you use to simplify

\sqrt{24}

a)

1

b)

4

c)

9

d)

16

2.

Simplify:

\sqrt{98}

a)

$7\sqrt{2}$

b)

$2\sqrt{7}$

c)

$49\sqrt{2}$

d)

$2\sqrt{49}$

3.

Simplify:

\sqrt{80x^2y^4}

a)

$2xy^2\sqrt{20}$

b)

$4xy^2\sqrt{5}$

4.

Simplify:

\sqrt{x^2y^7}

a)

$xy^3$

b)

$xy^3\sqrt{y}$

c)

$xy^3\sqrt{xy}$

5.

Simplify: $\left(\sqrt{10x}\right)\left(\sqrt{45x}\right)$

a)

$3\sqrt{50x}$

b)

$2x\sqrt{15}$

c)

$x\sqrt{450}$

d)

$15x\sqrt{2}$

6.

Simplify
3√6 - 4√6

a)

-√6

b)

√6

c)

-1

d)

Already simplified

7.

Simplify: $\frac{\sqrt[]{10x^5}}{\sqrt[]{2}}$

a)

$\frac{10}{2}$

b)

$5\sqrt[]{2x^5}$

c)

$x^2\sqrt[]{5x}$

d)

$2x\sqrt[]{5x}$

8.

Simplify: $\frac{\sqrt[]{2}}{4\sqrt[]{3}}$

a)

$\frac{\sqrt[]{15}}{9}$

b)

$\frac{2\sqrt[]{3}}{3}$

c)

$\frac{\sqrt[]{6}}{12}$

d)

$2\sqrt[]{6}$

9.

Solve

a)

d = 12

b)

d = -3 or d = 4

c)

d = -3

d)

d = 4

10.

Question 3

a)

20

b)

11

c)

4

d)

-2

11.

Question 1

a)

10

b)

8

c)

16

d)

4

12.

Solve.

a)

y = 3

b)

y = -3

c)

y = -1

d)

No Solution

13.

Simplify the radical...

√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

14.

Simplify

a)

A

b)

B

c)

C

d)

D

15.

√500x⁸y²

a)

10x⁴y√5

b)

10x⁴y²√5

c)

50x⁴y

d)

100x⁴y√5

16.

-3√80a⁷

a)

4a³√5a

b)

-12a³√5a

c)

-3a³√5a

d)

-48a³√5a

17.

a)

A

b)

B

c)

C

d)

D

18.

a)

A

b)

B

c)

C

d)

D

19.

a)

A

b)

B

c)

C

d)

D

20.

a)

A

b)

B

c)

C

d)

D

21.

a)

A

b)

B

c)

C

d)

D

22.

a)

A

b)

B

c)

C

d)

D

23.

a)

A

b)

B

c)

C

d)

D

24.

a)

A

b)

B

c)

C

d)

D

25.

a)

A

b)

B

c)

C

d)

D

26.

a)

A

b)

B

c)

C

d)

D

27.

Match the following

a)

1.

D:{x>=0}

R:{y>=0}

b)

2.

D:{x>=0}

R:{y<=0}

c)

3.

Not a function

d)

4.

D:{x<=0}

R:{y<=0}

e)

5.

D:{x<=0}

R:{y>=0}

28.

Match the following

a)

1.

Radical Function

R:{y>=2}

b)

2.

Quadratic Function

R:{y>=2}

c)

3.

Not a function

d)

4.

Quadratic Function

R:{y>=0}

e)

5.

Radical Function

R:{y>=0}

29.

Select all that apply

$y=\sqrt[]{x-3}-4$

a)

$D:\left\{x\ge3\right\}$

b)

$D:\left\{x\ge-3\right\}$

c)

$R:\left\{y\ge4\right\}$

d)

$R:\left\{y\ge-4\right\}$

e)

Starting point is (-3, -4)

30.

Select all that apply

$y=\sqrt[]{x+5}-2$

a)

$D:\left\{x\ge-5\right\}$

b)

$D:\left\{x\ge5\right\}$

c)

$R:\left\{y\ge2\right\}$

d)

$R:\left\{y\ge-2\right\}$

e)

Starting point is (-5, -2)

31.

Which equation is shown?

a)

$y=\sqrt[]{x-3}$

b)

$y=\sqrt[]{x+3}$

c)

$y=\sqrt[]{x}-3$

d)

$y=\sqrt[]{x}+3$

32.

Which equation is shown?

a)

$y=\sqrt[]{x-2}$

b)

$y=\sqrt[]{x+2}$

c)

$y=\sqrt[]{x}-2$

d)

$y=\sqrt[]{x}+2$

33.

What is the range of the given graph? Use correct notation.

(a)

34.

Match the following

a)

$y=a\left|x-h\right|+k$

1.

Absolute Value Function

b)

$y=a\left(x-h\right)^2+k$

2.

Quadratic Function in Vertex Form

c)

$y=ax^2+bx+c$

3.

Quadratic Function in Standard Form

d)

$y=a\sqrt[]{x-h}+k$

4.

Radical Function

e)

$y=mx+b$

5.

Linear Function

35.

Match the following

a)

1.

Absolute Value Function

b)

2.

Quadratic Function

c)

3.

Exponential Function

d)

4.

Radical Function

e)

5.

Linear Function

36.

Which is the graph of the following equation?

$y=\sqrt[]{x+4}$

a)

b)

c)

d)

37.

Which is the graph of the following equation?

$y=\sqrt[]{x+2}-2$

a)

b)

c)

d)

38.

Describe the transformation taking place in the given function

$f\left(x\right)=3\sqrt{x-2}+5$

a)

a stretch by a factor of 3 Shift right 2 Shift up 5

b)

a stretch by a factor of 3 Shift up 2 Shift right 5

c)

a shrink by a factor of 3 Shift down 2 Shift left 5

d)

A shrink by a factor of 3

Shift right 2 Shift down 5

39.

Which graph shows the following function?

f\left(x\right)=\sqrt{-x}+5

a)

b)

c)

d)

G8 Simplifying radicals and radical functions

Total questions: 39

Worksheet time: 1hrs 26mins

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