Free Printable ROOTS - Square & cube

1.

Write an equation for this phrase, "The square root of x is equal to 3."

a)

x² = 3

b)

x² = 9

c)

√x = 3

d)

√x = 9

2.

Solve for x when x= √16

a)

x = 2

b)

x = 4

c)

x = 8

d)

x = 32

3.

Solve for p when p² = 100.

a)

1,000

b)

10

c)

0.10

d)

-0.10

4.

Solve for x when x² = 144

a)

4

b)

11

c)

12

d)

14

5.

Solve for x when x = (3/4)²

a)

x = 4/3

b)

x = 9/4

c)

x = 9/16

d)

x = 3/16

6.

Solve for x when x³ = 125

a)

5

b)

10

c)

12

d)

15

7.

Solve for x when x³ = 1/8

a)

x = 2

b)

x = 1/2

c)

x = 4

d)

x = 16

8.

Write an equation for this phrase, "2 cubed is equal to the square root of x."

a)

2³ = √x

b)

2² = √x

c)

4 = √16

d)

√x = 2

9.

If x³ = -27, then x equals

a)

-3

b)

-9

c)

+3 and -3

d)

+9 and -9

10.

A cube with side length s has a volume of 64 cubic units. What is the length of the side of the cube?

a)

32 units

b)

16 units

c)

8 units

d)

4 units

11.

A square with side length s has an area of 0.81 square units. What is the length of the side of the square?

a)

0.9 units

b)

0.6561 units

c)

0.405 units

d)

0.3 units

12.

The volume of a cube is 1,000 cm³. What is the length of each side of the cube?

a)

1

b)

10

c)

100

d)

300

13.

Select the answer with all perfect squares.

a)

-144, 9, 50, 75, 81, 100

b)

9, 50, 75, 81, 100

c)

9, 50, 81, 100

d)

9, 81,100

14.

The area of a square is 400 m². What is the length of the side of the square?

a)

20 m

b)

200 m

c)

20 m²

d)

200 m²

15.

THINK! Solve for x when √x = 2²

a)

2

b)

4

c)

8

d)

16

16.

The number -8 is a

a)

perfect Square

b)

perfect Cube

17.

The number 16 is a

a)

perfect square

b)

perfect cube

18.

The number 25/9 is a

a)

perfect square

b)

perfect cube

19.

The number -27/64 is a

a)

perfect square

b)

perfect cube

20.

The number 1000 is

a)

perfect square

b)

perfect cube

21.

a)

8

b)

9

c)

10

d)

11

22.

a)

9

b)

3

c)

1/3

d)

1

23.

In the picture, the "3" is called...

a)

the index

b)

the radical sign

c)

the radicand

d)

none

24.

What kind of number is the cube root of 100.

a)

Rational

b)

irrational

25.

What type of number is the square root of 25?

a)

rational

b)

irrational

26.

√-25

a)

5

b)

-5

c)

±5

d)

None

27.

√1

a)

2

b)

1

c)

10

d)

11

28.

What is a square root??

a)

You have to multiply to get the square root

b)

Multiply to get an odd number.

c)

the square root of a number is the factor that we can multiply by itself to get that number.

d)

Multiply and divide to get the square root

29.

What is the square root of 225??

a)

16

b)

15

c)

9

d)

8

30.

Estimate the square root.

a)

4

b)

5

c)

6

d)

7

31.

Estimate the square root.

a)

4

b)

5

c)

6

d)

7

32.

Estimate the square root.

a)

7

b)

8

c)

9

d)

10

33.

Between which two whole numbers is the
√20 ?

a)

5 and 6

b)

10 and 2

c)

4 and 5

d)

3 and 4

34.

Find the value of

a)

b)

c)

d)

35.

Perimeter of a square field is 164 m. Find the area of the field.

a)

41

b)

82

c)

1681

d)

1730

36.

Which number in this list is not a rational number?

√5, ∛8, 0, -4.2

a)

√5

b)

∛8

c)

0

d)

-4.2

37.

Identify the base and the exponent of 4a⁵

a)

base is a, exponent is 5

b)

base is 4a, exponent is 5

c)

base is 5, exponent is a

d)

base is 5, exponent is 4a

38.

Expand and evaluate -3⁴

a)

-3 * 3 * 3 * 3 = -81

b)

-3 * -3 * -3 * -3 = 81

c)

-3 * 3 * 3 * 3 = 81

d)

-3 * -3 * -3 * -3 = -81

39.

Write in exponential notation: -4 * -4 * -4

a)

(-4)³

b)

-4³

c)

-(4)³

d)

-64

40.

Simplify -3⁰

a)

-1

b)

1

c)

0

d)

-3

41.

Write 5^-2 as a simple fraction or integer.

a)

1/25

b)

-25

c)

-1/25

d)

25

42.

Rewrite 5x^-2y^-3 using only positive exponents.

a)

5/(x²y³)

b)

5x²y³

c)

5x^-2y^-3

d)

1/(5x²y³)

43.

Simplify

a)

x²y√xy

b)

xy

c)

x²y²

d)

Can't Simplify

44.

CHALLENGE.

a)

3

b)

62

c)

6

d)

2

45.

Find the cube root.

a)

-10

b)

10

c)

100

d)

-100

46.

What is a square?

a)

Something you multiply by the 3rd power

b)

A trianglular shape

c)

A number you multiply by itself

47.

In between what two integers is the square root of 77?

a)

5 and 6

b)

6 and 7

c)

7 and 8

d)

8 and 9

48.

In between what two integers is the square root of 44?

a)

3 and 4

b)

4 and 5

c)

5 and 6

d)

6 and 7

49.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

ROOTS - Square & cube

Total questions: 49

Worksheet time: 51mins

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