Question

Find the cube root of each of the following numbers by prime factorisation method.

1. 175616 (2) 91125

Answer 1

(i)175616

The given number is 175616.

After resolving the prime factors by prime factorisation, we get

175616 = 2×2×2×2×2×2×2×2×2×7×7×7

Upon grouping the factors we get,

175616 = (2×2×2)×(2×2×2)×(2×2×2)×(7×7×7)

Taking one factor from each group

1756163 = 2 x 2 x 2 x 7 =56

Hence, the required cube root is 56.

(ii)91125

The given number is 91125.

After resolving the prime factors by prime factorisation, we get

91125 = 3×3×3×3×3×3×3×5×5×5

Upon grouping the factors we get,

91125 = (3×3×3)×(3×3×3)×(5×5×5)

Taking one factor from each group

91125 = 3 x 3 x 5 = 45