Cubing a Number

True or false: To cube a number, multiply it by itself three times. For example, if you have the number 3, cubing it means multiplying 3 by 3 by 3, which equals 27.

• True

• False

Answer explanation

When you cube a number, you multiply it by itself three times. For example, if you have the number 3, cubing it means 3 multiplied by 3 multiplied by 3, which equals 27. So, 3³ = 3 × 3 × 3 = 27.

True or false: When you cube a negative number, you get a positive result because a negative times a negative times a negative gives a positive. For instance, if you cube -4, you get -4 × -4 × -4 = 64.

• True

• False

Answer explanation

When you cube a negative number, you get a negative result because a negative times a negative times a negative gives a negative. For example, if you cube -4, you get -4 × -4 × -4 = -64, which is negative. So, (-4)³ = -4 × -4 × -4 = -64.

True or false: A perfect cube is a number that you get when you multiply a whole number by itself three times. For example, 27 is a perfect cube because it can be obtained by multiplying 3 (a whole number) by itself three times: 3 × 3 × 3 = 27.

• True

• False

Answer explanation

A perfect cube is a number that you get when you multiply a whole number by itself three times. For example, 27 is a perfect cube because it can be obtained by multiplying 3 (a whole number) by itself three times: 3 × 3 × 3 = 27.

The volume of a cube can be found by cubing the side length. A cube has a side length of 4 cm. What equation represents the volume of the cube?

• V = 4³ = 16

• V = 4 × 3 = 12

• V = 4³ = 64

• V = 4 × 2 = 8

Answer explanation

The formula for finding the volume of a cube is given by V = side³ = side length × side length × side length. In this case, the side length is 4 cm. So, the correct equation is V = 4³ = 4 × 4 × 4 = 64.

Evaluate 5³.

• 15

• 49

• 21

• 125

Answer explanation

To find 5³, you need to multiply 5 by itself three times: 5 × 5 × 5 = 125. So, 5³ = 125.

Evaluate (-3)³.

• 9

• -27

• 33

• -9

Answer explanation

To find (-3)³, you need to multiply -3 by itself three times: -3 × -3 × -3 = -27. So, (-3)³ = -27.

Evaluate -6³.

• -216

• 216

• -18

• 18

Answer explanation

To find -6³, you need to cube 6 (6 × 6 × 6), which equals 216. Then, you add the negative sign, resulting in -216. So, -6³ = -216.

Evaluate (1/2)³.

• 1/2

• 1/4

• 1/8

• 1/16

Answer explanation

To find (1/2)³, you cube both the numerator and the denominator separately: (1³)/(2³) = 1/8. So, (1/2)³ = 1/8.

Evaluate (-0.7)³.

• -0.729

• 0.49

• 0.343

• -0.343

Answer explanation

To find (-0.7)³, you cube the decimal value: -0.7 × -0.7 × -0.7 = -0.343. So, (-0.7)³ = -0.343.

Evaluate -(5/6)³.

• 125/216

• -125/216

• 125/196

• -125/196

Answer explanation

To find - (5/6)³, first cube the fraction. You cube both the numerator and the denominator separately: (5³)/(6³) = 125/216. Then, add the negative sign, resulting in -(125/216). So, -(5/6)³ = -125/216.