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Class 8 Cube Root by Prime Factorisation — 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 the cube root of 8 by prime factorisation.
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Answer: A) 2
8 = 2 x 2 x 2 = 2³. Grouping one triple of 2, cube root = 2.
2. Find the cube root of 1331 by prime factorisation.
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Answer: A) 11
1331 = 11 x 11 x 11 = 11³. Cube root = 11.
3. Using cube root by prime factorisation, find the value of cube root of 64 multiplied by cube root of 27.
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Answer: D) 12
Cube root of 64 = 4, cube root of 27 = 3. Product = 4 x 3 = 12. (Also cube root of 64 x 27 = cube root of 1728 = 12.)
4. The volume of a cubical storage room in a Chennai warehouse is 91125 cubic feet.
Find the length of one wall (the edge) in feet using prime factorisation.
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Answer: A) 45
91125 = 3⁶ x 5³ = (3² x 5)³ = 45³. Edge = cube root = 45 feet.
5. The number 137592 is not a perfect cube.
Its prime factorisation is 137592 = 2³ x 3⁴ x 7³.
Find the smallest number it must be divided by to give a perfect cube, and the cube root of the result.
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Answer: A) divide by 3, cube root 42
137592 = 2³ x 3⁴ x 7³. The 3 has exponent 4; remove one 3 (divide by 3) to leave 3³. Result = 2³ x 3³ x 7³ = (2 x 3 x 7)³ = 42³, cube root = 42.
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