Q. 5 D3.5( 2 Votes )

# Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube.

675

Answer :

675

Prime Factorization:

⇒ 675 = 5 × 5 × 3 × 3 × 3

= 3^{3} × 5^{2}

There are only two 5’s.

∴ 675 is not a perfect cube.

To make it a perfect cube, we multiply with 5.

⇒ 675 × 5 = 3375

= 5 × 5 × 5 × 3 × 3 × 3

= 3^{3} × 5^{3}

= 15^{3} which is a perfect cube

∴ The smallest number by which the number 675 must be multiplied to obtain a perfect cube is 5.

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