Cube Rooting a Number

True or false: To cube root a number, find the value that, when multiplied by itself three times, equals the original number. For example, the cube root of 27 is 3 because 3 multiplied by itself three times equals 27 (3 × 3 × 3 = 27).

• True

• False

Answer explanation

If you have a number, like 27, and you want to find its cube root, you're basically looking for a number that, when you multiply it by itself three times, equals 27. In this case, the cube root of 27 is 3 because 3 multiplied by itself three times (3 × 3 × 3) equals 27. So, cube rooting a number means finding a value that, when multiplied by itself three times, gives you the original number.

True or false: Taking the cube root of a negative number gives you a positive result. For example, the cube root of -64 is 4.

• True

• False

Answer explanation

This statement is false because taking the cube root of a negative number gives a negative result. The reason is that when you multiply a negative number by itself three times the result is always negative. For example, -4 × -4 × -4 = -64, so the cube root of -64 is -4.

True or False: A non-perfect cube root is the cube root of a number that is not a perfect cube, meaning it doesn't result in a whole number. For example, the cube root of 7 is a non-perfect cube root because it’s not a whole number or an exact decimal.

• True

• False

Answer explanation

A non-perfect cube root refers to the cube root of a number that is not a perfect cube. Perfect cubes have whole number cube roots, while non-perfect cube roots may result in decimals or fractions. For example, the cube root of 7 is a non-perfect cube root because it’s not a whole number or an exact decimal. The cube root of 7 is approximately 1.912931... which is an irrational number, meaning its decimal values go on forever without repeating.

The side length of a cube can be found by taking the cube root of its volume. A cube has a volume of 64 cubic units. What equation represents the side length of the cube?

• s = ∛64 = 5

• s = 5³ = 64

• s = ∛64 = 4

• s = 4³ = 12

Answer explanation

The formula for the side length (s) of a cube, given its volume (V), is s = ∛V. In this case, the volume is 64 cubic units. In this case, the volume is 64 cubic units and the cube root of 64 is 4 because 4 × 4 × 4 = 64. So, the equation representing the side length is s = ∛64 = 4.

What is ∛8000?

• 25

• 20

• 15

• 80

Answer explanation

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In this case, the cube root of 8000 is 20 because 20 × 20 × 20 equals 8000. So, ∛8000 = 20.

What is ∛0.125?

• 0.25

• 0.1

• 0.375

• 0.5

Answer explanation

The cube root of a number is a value that, when multiplied by itself three times, equals the original number. In this case, the cube root of 0.125 is 0.5 because 0.5 × 0.5 × 0.5 equals 0.125. So, ∛0.125 = 0.5.

What is ∛1/216?

• 1/6

• 1/8

• 1/12

• -1/6

Answer explanation

To take the cube root of a fraction, take the cube root of the numerator and the cube root of the denominator separately. In this case, ∛1 = 1 and ∛216 = 6. So, ∛1/216 = ⅙.

What is ∛-8?

• -4

• 2

• -2

• 4

Answer explanation

The cube root of a number is a value that, when multiplied by itself three times, equals the original number. In this case, the cube root of -8 is -2 because -2 × -2 × -2 = -8. So, ∛-8 = -2.

What is -∛343/1000?

• 7/1000

• -7/10

• 7/10

• -7/1000

Answer explanation

To take the negative cube root of a fraction, first take the cube root of the numerator and the cube root of the denominator separately. In this case, ∛343 = 7 and ∛1000 = 10, which give you 7/10. Then add a negative sign, so -∛343/1000 = -7/10.

What is -∛-0.000027?

• -0.03

• 0.09

• -0.09

• 0.03

Answer explanation

To take the negative cube root of a negative number, first find a value that, when multiplied by itself three times, equals the original number. In this case, the cube root of -0.000027 is -0.03 because -0.03 × -0.03 × -0.03 equals -0.000027. Then add a negative sign, -(-0.03), which equals 0.03 because the negative of a negative is a positive. So -∛-0.000027 = 0.03.