8th Grade Square Roots and Cube Roots Test with Point Values (PDF)

8th Grade math test: Square Roots and Cube Roots – Maths PDF

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This square cube roots test for 8th Grade covers square roots and cube roots (Common Core 8.EE.A.2), with a free PDF to print.

This 20-point test checks square roots, cube roots and equations of the form x squared or x cubed equals p (Common Core 8.EE.A.2). Work alone, show every step, and write each final answer clearly. You have 45 minutes. Calculators are not needed unless a question says so.

Time and points

About this test

Grade: Grade 8
Chapter: Square Roots and Cube Roots
Standards: 8.EE.A.2
Time: 45 minutes
Total: 20 points

Square cube roots test: questions

Question 1 – Evaluate roots [2 pts]

Evaluate \(\sqrt{169}\). (1 point)
Evaluate \(\sqrt[3]{343}\). (1 point)

Question 2 – Roots of fractions [2 pts]

Evaluate \(\sqrt{\frac{9}{49}}\). (1 point)
Evaluate \(\sqrt[3]{\frac{1}{64}}\). (1 point)

Question 3 – Solve [3 pts]

Solve \(x^{2} = 81\). (1 point)
Solve \(x^{3} = 125\). (1 point)
Is \(x = 9\) the only solution of part a? Explain. (1 point)

Question 4 – Solve with a coefficient [2 pts]

Solve \(5x^{2} = 80\).

Question 5 – Square plot [3 pts]

A square plot of land with area 400 square meters.

Find the side length of the plot, then the length of fence needed to enclose it.

Question 6 – Cube tank [3 pts]

Cube-shaped tank.

A cube-shaped tank holds 64 cubic feet of water. Find its edge length and the area of its square base.

Question 7 – Estimate [3 pts]

The point ? marks the square root of 60.

Between which two integers is \(\sqrt{60}\)? (1 point)
Estimate \(\sqrt{60}\) to the nearest tenth. (1 point)
Is \(\sqrt{60}\) rational? Explain. (1 point)

Question 8 – Two solutions [2 pts]

Explain why \(x^{2} = 9\) has two solutions but \(x^{3} = 8\) has one real solution. Use numbers in your explanation.

Key facts behind this square cube roots test

Key facts

\(\sqrt{81} = 9\) because \(9^{2} = 81\); \(\sqrt[3]{125} = 5\) because \(5^{3} = 125\).
\(x^{2} = p\) with \(p > 0\) has two solutions: \(x = \pm\sqrt{p}\).
\(x^{3} = p\) has one real solution: \(x = \sqrt[3]{p}\).
Know the perfect squares up to \(15^{2}\) and the perfect cubes up to \(5^{3}\).
Roots of non-perfect squares, like \(\sqrt{20}\), are irrational and can be estimated.

How to use this square cube roots test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 8 chapters: Grade 8 math.

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