This grade 8 square test answer key gives the full solution and the scoring guide for each of the 9 test questions on square roots and cube roots.
Use this answer key to score the square roots and cube roots test. Each solution is worked out, and a scoring note explains how to award the points. Give partial credit when the method is right and only the arithmetic slips. The total is 20 points.
Grade 8 Square Test Answer Key: questions 1–5
Question 1: Evaluate roots (2 points)
- \(11\cdot11=121\), so \(\sqrt{121}=11\).
- \(6\cdot6\cdot6=216\), so \(\sqrt[3]{216}=6\).
Scoring: 1 point for each correct value.
Question 2: Solve with whole numbers (2 points)
- \(15\cdot15=225\), so \(x=15\) or \(x=-15\).
- \((-5)^{3}=-125\), so \(x=-5\).
Scoring: part (a) 1 point, and both solutions are required; part (b) 1 point.
Question 3: Fractions and decimals (2 points)
- \(0.6\cdot0.6=0.36\), so \(x=0.6\) or \(x=-0.6\).
- \(\sqrt[3]{1}=1\) and \(\sqrt[3]{64}=4\), so \(x=\frac{1}{4}\).
Scoring: 1 point for each part; part (a) needs both signs.
Question 4: Square picture frame (2 points)
- \(\sqrt{81}=9\), so the side is 9 in.
- \(4\cdot9=36\), so the perimeter is 36 in.
Scoring: 1 point for the side with units, 1 point for the perimeter with units.
Question 5: Cube-shaped box (2 points)
- \(\sqrt[3]{512}=8\), since \(8^{3}=512\). The edge is 8 in.
- One face is 8 in by 8 in: \(8^{2}=64\) square inches.
Scoring: 1 point for the edge, 1 point for the face area with square units.
Grade 8 Square Test Answer Key: questions 6–9
Question 6: Estimate between integers (2 points)
- \(8^{2}=64<72<81=9^{2}\), so between 8 and 9.
- \(3^{3}=27<30<64=4^{3}\), so between 3 and 4.
Scoring: 1 point for each pair; the pair must be consecutive integers.
Question 7: Square with area 2 (2 points)
- The side \(s\) satisfies \(s^{2}=2\), so \(s=\sqrt{2}\) in.
- The number \(\sqrt{2}\) is irrational. Since \(1.4^{2}=1.96<2<2.25=1.5^{2}\), it lies between 1.4 and 1.5.
Scoring: 1 point for \(\sqrt{2}\); 1 point for irrational with the interval between 1.4 and 1.5.
Question 8: Border for a patio (3 points)
- \(\sqrt{400}=20\), so each side is 20 ft.
- \(4\cdot20=80\) ft of border.
- \(80\cdot3.50=280\), so the cost is $280.00.
Scoring: 1 point for each part; carry-forward credit if the side is wrong but later steps follow from it.
Question 9: Shipping crate (3 points)
- \(\sqrt[3]{3375}=15\), since \(15^{3}=3375\). The edge is 15 in.
- \(15^{2}=225\) square inches.
- The crate is 15 in on each edge, and 15 is greater than 14, so it does not fit.
Scoring: 1 point for each part; part (c) needs the comparison 15 greater than 14.
Scoring summary
20 points: add the points of every question of this grade 8 square test answer key.
How to use this grade 8 square test answer key
Use this grade 8 square test answer key to score the test fairly and to see which skills need more practice.
See every chapter on the Grade 8 math page.
