Class 8 Cubes and Cube Roots — practice questions with answers

Cubes and Roots · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Find

364

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Answer: B) 4

4³ = 64. So

364

= 4.

2. Find

33375

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Answer: A) 15

3375 = 3³ × 5³ = (3 × 5)³ = 15³. So

33375

= 15.

3. Which of the following numbers, when cubed, gives a value ending in the digit 7?

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Answer: B) 3

3³ = 27 ends in 7. (2³ = 8, 8³ = 512 ends in 2, 9³ = 729 ends in 9.)

4. Find

3 \frac{216}{343}

A $\frac{6}{7}$
B $\frac{7}{6}$
C $\frac{36}{49}$
D $\frac{72}{343}$

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Answer: A)

\frac{6}{7}

Cube-root the numerator and the denominator separately: 216 = 6³ and 343 = 7³, so the answer is

\frac{6}{7}

. The option

\frac{72}{343}

divides the numerator by 3 instead of taking its cube root, and

\frac{36}{49}

squares 6 and 7 rather than leaving them alone.

5. Rani needs the largest whole number whose cube is still less than 500. Which number is it?

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Answer: D) 7

7³ = 343 is under 500 while 8³ = 512 goes over, so 7 is the largest. Answering 22 uses the square root of 500 (about 22.4) instead of the cube root, and 6 stops one step early at 216.

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