Find the cube root of 512 by prime factorisation method.

Solution

We have to find the cube root of 512 by prime factorisation method

512 = 2×2×2×2×2×2×2×2×2

By assortingthe factors in triplets of equal factors, 512 = (2×2×2)×(2×2×2)×(2×2×2)

Here, 512 can be arranged into triplets of equal factors,

∴ 512 = 2×2x 2 = 8

Answer

Hence, 8 is cube root of 512.

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