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प्रश्न
Using prime factorisation, find which of the following are perfect cubes.
128
उत्तर
We have, 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
Since, 2 remains after grouping in triplets.
So, 128 is not a perfect cube.
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संबंधित प्रश्न
Find the cube root of the following numbers by the prime factorisation method.
27000
You are told that 1331 is a perfect cube. Can you guess without factorization what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768
\[\sqrt[3]{8 \times . . .} = 8\]
\[\sqrt[3]{480} = \sqrt[3]{3} \times 2 \times \sqrt[3]{. . .}\]
\[\sqrt[3]{. . .} = \sqrt[3]{4} \times \sqrt[3]{5} \times \sqrt[3]{6}\]
Evaluate:
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250.
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34.2 .
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By what smallest number should 3600 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient.
