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Square Roots and Cube Roots Test – Grade 8 Math (Printable PDF)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Grade 8 Math Tests – Mathbot, the Math Made Easy robot coach, with free printable tests for Grade 8
Looking for a square roots and cube roots test PDF? Then this Grade 8 test on Solving With Square and Cube Roots checks the whole chapter, with points for each question. This test has 8 questions worth 20 points in total and should take about 45 minutes. Show your steps for every question and use exact roots unless an approximation is requested. A calculator is not required.

Standards: 8.EE.A.2 · Level: Grade 8

Time: 45 minutes · 8 questions · Total: 20 points · Calculator: as allowed by your teacher

Question 1 Evaluate the roots (3 points)

Evaluate each root. (1 point each)

  1. √196
  2. ∛(−343)
  3. √4981

Question 2 Solve for x (3 points)

Solve each equation. (1 point each)

  1. x² = 144
  2. x³ = −216
  3. x² = 0.49

Question 3 Between integers (2 points)

Between which two consecutive integers does each number lie? (1 point each)

  1. √75
  2. ∛75

Question 4 Storage bin (3 points)

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

  1. Find the edge length. (1 point)
  2. Find the area of one face. (1 point)
  3. Find the total surface area. (1 point)
V = 512 in³
Storage bin.

Question 5 Two-step equations (3 points)

Solve each equation.

  1. 3x² − 20 = 127 (2 points)
  2. 2x³ + 6 = 134 (1 point)

Question 6 Square deck (3 points)

A square deck has an area of 135 square feet.

  1. Between which two consecutive integers is the side length? (1 point)
  2. Find the side length to the nearest tenth of a foot. (1 point)
  3. Is the side length a rational number? Explain. (1 point)
135 ft²side = s
Square deck.

Question 7 Check Dan’s claim (2 points)

Dan says that x² = −25 has the solution x = −5. Explain whether he is right.

Question 8 Compare (1 point)

Is √50 less than or greater than 7.1? Justify with a square.

View the Square Roots And Cube Roots test answer key with scoring

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