Q. 5 A5.0( 2 Votes )

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

243

Answer :

243

Prime Factorization:

⇒ 243 = 3 × 3 × 3 × 3 × 3

= 3^{3} × 3^{2}

There are only two 3’s.

∴ 243 is not a perfect cube.

To make it a perfect cube, we multiply it with 3.

⇒ 243 × 3 = 729

= 3 × 3 × 3 × 3 × 3 × 3

= 3^{3} ×3^{3} which is a perfect cube

∴ The smallest number by which the number 243 must be multiplied to obtain a perfect cube is 3.

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