Square Roots and Cube Roots: Grade 8 Math Test – PDF Download

Question 1: Evaluate roots (2 points)

1. Evaluate \(\sqrt{121}\). (1 point)
2. Evaluate \(\sqrt[3]{216}\). (1 point)

Question 2: Solve with whole numbers (2 points)

1. Solve \(x^{2}=225\). (1 point)
2. Solve \(x^{3}=-125\). (1 point)

Question 3: Fractions and decimals (2 points)

1. Solve \(x^{2}=0.36\). Give both solutions. (1 point)
2. Solve \(x^{3}=\frac{1}{64}\). (1 point)

Question 4: Square picture frame (2 points)

A square picture has an area of 81 square inches.

1. Find the side length. (1 point)
2. Find the perimeter. (1 point)

Question 5: Cube-shaped box (2 points)

A cube-shaped box has a volume of 512 cubic inches.

1. Find the edge length. (1 point)
2. Find the area of one face. (1 point)

Question 6: Estimate between integers (2 points)

1. Between which two consecutive integers is \(\sqrt{72}\)? (1 point)
2. Between which two consecutive integers is \(\sqrt[3]{30}\)? (1 point)

Question 7: Square with area 2 (2 points)

A square has an area of 2 square inches.

1. Write the side length using a radical. (1 point)
2. Is the side length rational or irrational? Between which two tenths does it lie? (1 point)

Question 8: Border for a patio (3 points)

Priya’s square patio has an area of 400 square feet. She wants to trim all four edges with border stones that cost $3.50 per foot.

1. Find the side length. (1 point)
2. Find the total length of border needed. (1 point)
3. Find the cost. (1 point)

Question 9: Shipping crate (3 points)

Ethan’s cube-shaped crate holds 3,375 cubic inches.

1. Find the edge length of the crate. (1 point)
2. Find the area of the floor of the crate. (1 point)
3. A shelf is 14 inches deep. Does the crate fit on it with its edge along the depth? Explain. (1 point)

⬇ Download the Grade 8 Square Roots and Cube Roots test (PDF, 83 KB)

See every chapter on the Grade 8 math page.