Question

find cube root of 27000 by prime factorization​

Answer 1

⇒27000=2×2×2×3×3×3×5×5×5

On forming pairs of three

⇒ 27000=2cube×3cube×5cube

On taking cube root on both side

⇒(27000)−−−−−−√3=(2×3×5)3−−−−−−−−−−√3

Cube root can be write raised to power 13

⇒27000−−−−−√3=(2×3×5)3×13

On cancelling exponential power

⇒ So cube root of 27000 = 2×3×5=30