Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Begin with the easy roots and move toward estimates and real measurements. Give exact answers first, then approximations when a question asks for them.
Standards: 8.EE.A.2 · Level: Grade 8
Problem 2 Evaluate cube roots ★★★
Evaluate: (a) ∛27 (b) ∛125 (c) ∛(−8) (d) ∛18
Problem 3 Spot the perfect squares ★★★
Which of these numbers are perfect squares: 48, 81, 100, 150, 196?
Problem 4 Spot the perfect cubes ★★★
Which of these numbers are perfect cubes: 9, 64, 100, 216, 1,000?
Problem 5 Two small equations ★★★
Solve: (a) x² = 49 (b) x³ = 125
Problem 6 Patio side length ★★★
A square patio has an area of 169 square feet. How long is each side?
Problem 7 Fractions and decimals ★★★
Solve: (a) x² = 81100 (b) x² = 0.16
Problem 8 Negative and fractional cubes ★★★
Solve: (a) x³ = −64 (b) x³ = 27343
Problem 9 A root that is not whole ★★★
Solve x² = 50. Give the exact solutions and approximate each to the nearest hundredth.
Problem 10 A cube root estimate ★★★
Solve x³ = 30 and estimate the answer to the nearest tenth.
Problem 11 Cube-shaped box ★★★
A cube-shaped gift box holds 216 cubic inches. Find its edge length.
Problem 12 Two-step equations ★★★
Solve: (a) 2x² = 98 (b) x³ + 5 = 69
Problem 13 Estimate two roots ★★★
Estimate to the nearest tenth: (a) √200 (b) ∛100
Problem 14 Solutions on a number line ★★★
The two orange points show the solutions of x² = 20. Write the solutions exactly and estimate each to the nearest tenth.
Problem 15 Mural frame ★★★
A square mural has an area of 289 square feet. A frame around its edge costs $3.25 per foot. Find the side length, the perimeter and the cost of the frame.
Problem 16 Storage cube surface ★★★
A cube-shaped bin has a volume of 343 cubic centimeters. Find the edge length and the total surface area.
Problem 17 Garden fence ★★★
A square garden has an area of 90 square feet. Estimate the amount of fencing needed to enclose it, to the nearest tenth of a foot.
Problem 18 Why is √2 irrational? ★★★
Show that √2 lies between 1.41 and 1.42, then explain what it means that √2 is irrational.
Problem 19 Two cubes ★★★
Cube A has an edge of 6 inches. Cube B has a volume of 300 cubic inches. Which cube has the longer edge, and by about how much to the nearest tenth?
Problem 20 Check a claim ★★★
Dan says both x² = −16 and x³ = −64 have the solution −4. Decide whether each claim is right and explain.
