A square has an area of \(361\) square cm. What is its perimeter?
- \(38\) cm
- \(57\) cm
- \(76\) cm
- \(152\) cm
Testinar Grade 8 math
Square Roots and Cube Roots
Learn to reason about and solve Grade 8 problems involving Square Roots and Cube Roots.
CH02-02
Exponents, Roots, and Scientific Notation
- Name
- Date
- Score
- ____ / 8
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If a cube has a side length of \(5\) cm, what is its volume?
- \(15\) cm\(^3\)
- \(25\) cm\(^3\)
- \(75\) cm\(^3\)
- \(125\) cm\(^3\)
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Between which two consecutive integers does \(\sqrt[3]{50}\) lie?
- \(2\) and \(3\)
- \(5\) and \(6\)
- \(4\) and \(5\)
- \(3\) and \(4\)
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Which is a reasonable approximation for \(\sqrt{200}\)?
- \(12\)
- \(18\)
- \(16\)
- \(14\)
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If the volume of a cube is \(343\) cm\(^3\), what is the surface area of one face?
- \(7\) cm\(^2\)
- \(294\) cm\(^2\)
- \(98\) cm\(^2\)
- \(49\) cm\(^2\)
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What is \(\sqrt[3]{125}\)?
- \(25\)
- \(11\)
- \(15\)
- \(5\)
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Which of the following is a perfect square?
- \(48\)
- \(99\)
- \(75\)
- \(64\)
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What is \(\sqrt{400}\)?
- \(18\)
- \(19\)
- \(20\)
- \(21\)
Answer key and explanations
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C. \(76\) cm
Area \(= 361\), so \(s = \sqrt{361} = 19\) cm. Perimeter \(= 4s = 4 \times 19 = 76\) cm.
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D. \(125\) cm\(^3\)
Volume of a cube \(= s^3 = 5^3 = 125\) cm\(^3\).
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D. \(3\) and \(4\)
\(3^3 = 27\) and \(4^3 = 64\). Since \(27 < 50 < 64\), we have \(3 < \sqrt[3]{50} < 4\).
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D. \(14\)
\(\sqrt{200} = \sqrt{100 \times 2} = 10\sqrt{2} \approx 10 \times 1.41 = 14.1\). So \(14\) is the closest integer.
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D. \(49\) cm\(^2\)
Volume \(= s^3 = 343\), so \(s = \sqrt[3]{343} = 7\) cm. One face is a square with side \(7\) cm, so area \(= 7^2 = 49\) cm\(^2\).
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D. \(5\)
\(5\times5\times5=125\), so \(\sqrt[3]{125}=5\).
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D. \(64\)
\(\sqrt{64} = 8\). The other numbers are not perfect squares.
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C. \(20\)
\(20 \times 20 = 400\), so \(\sqrt{400} = 20\).
