These problems practice Common Core standard 8.EE.A.2: evaluating square roots and cube roots of perfect squares and perfect cubes, and solving equations of the form \(x^{2}=p\) and \(x^{3}=p\). Early problems use whole numbers, then fractions and decimals.
The last seven problems are word problems about squares and cubes, including two estimates for numbers that are not perfect squares or cubes. Work from easiest to hardest.
Problem 1: Square root of 49
Evaluate \(\sqrt{49}\).
Problem 2: Square root of 144
Evaluate \(\sqrt{144}\).
Problem 3: Cube root of 27
Evaluate \(\sqrt[3]{27}\).
Problem 4: Cube root of 125
Evaluate \(\sqrt[3]{125}\).
Problem 5: Cube root of a negative
Evaluate \(\sqrt[3]{-64}\).
Problem 6: Two square roots
Solve \(x^{2}=81\).
Problem 7: A cube equation
Solve \(x^{3}=216\).
Problem 8: Another square equation
Solve \(x^{2}=169\).
Problem 9: A negative cube
Solve \(x^{3}=-343\).
Problem 10: Fraction square
Solve \(x^{2}=\frac{4}{25}\).
Problem 11: Fraction cube
Solve \(x^{3}=\frac{8}{27}\).
Problem 12: Decimal square
Solve \(x^{2}=0.64\).
Problem 13: Decimal cube
Solve \(x^{3}=0.001\).
Problem 14: Undo, then take the root
Solve \(x^{2}+6=70\).
Problem 15: Between two integers
Between which two consecutive integers is \(\sqrt{50}\)? Mark where it belongs on the number line.
Problem 16: Cube root estimate
Between which two consecutive integers is \(\sqrt[3]{100}\)?
Problem 17: Which number is irrational?
Exactly one of \(\sqrt{36}\), \(\sqrt{2}\), \(\sqrt[3]{8}\), \(\sqrt{100}\) is irrational. Name it and explain how the others are rational.
Problem 18: Compare a root and a decimal
Is \(\sqrt{30}\) less than or greater than 5.5? Show your reasoning.
Problem 19: Square garden fence
Maya’s square garden has an area of 196 square feet. She puts a fence around all four sides. Find the side length and the total length of fence.
Problem 20: Gift box
A cube-shaped gift box holds 343 cubic inches. Find the edge length and the area of one face.
Problem 21: Square rug fringe
A square rug has an area of 20.25 square feet. Fringe costs $1.50 per foot and goes on all four sides. Find the side length and the cost of the fringe.
Problem 22: Storage cube
A cube-shaped storage bin holds 1,728 cubic inches. Find its edge length in inches, then in feet.
Problem 23: Playground laps
A square playground has an area of 2,500 square feet. Jamal jogs 3 laps around its edge. How far does he jog?
Problem 24: Side of a square patio
Sofia’s square patio has an area of 50 square feet. Estimate its side length to the nearest tenth of a foot.
Problem 25: Edge of a small cube
A cube has a volume of 40 cubic inches. Estimate its edge length to the nearest tenth of an inch.
See every chapter on the Grade 8 math page.