8th Grade Square Roots and Cube Roots Quiz: 10 Questions with Explanations

A \(12\)B \(14\)C \(84.5\)D \(13\)

\(13 \cdot 13 = 169\). Halving 169 is a common mistake.

A \(8\)B \(7\)C \(16\)D \(170\)

\(8^{3} = 512\). Dividing by 3 is a typical error.

A \(x = 8\)B \(x = 32\)C \(x = \pm 8\)D \(x = \pm 32\)

Both 8 and -8 square to 64. Dividing by 2 gives the wrong 32.

A 12 ftB 11 ftC 60.5 ftD 121 ft

\(11^{2} = 121\).

A 7 and 8B 8 and 9C 9 and 10D 37 and 38

\(8^{2} = 64\) and \(9^{2} = 81\). 75 lies between 64 and 81.

A 25 inB 15 inC 5 inD 62.5 in

\(5^{3} = 125\), so the edge is 5 inches.

A \(x = 3\)B \(x = 27\)C \(x = 9\)D \(x = \pm 3\)

Divide by 3 to get \(x^{3} = 27\), so \(x = 3\). A cube has one real solution.

A 75 ftB 12.2 ftC 15 ftD 37.5 ft

The side is the square root of 150, about 12.2, because 12.2 squared is about 148.8 and 12.3 squared is 151.3. Dividing by 2 or by 4 is a common mistake.

A 120 mB 30 mC 60 mD 900 m

Side = 30 m, so perimeter = 4 x 30 = 120 m. Stopping at 30 is a common mistake.

A \(\sqrt{2} = 1.4\)B \(\sqrt{2} = \frac{3}{2}\)C \(\sqrt{2} \text{ is a whole number}\)D \(\sqrt{2} \text{ is irrational}\)

\(1.4^{2} = 1.96\) and \(1.5^{2} = 2.25\), so \(\sqrt{2}\) is between them and never ends or repeats.