Question

Find the smallest number by which 243 must be multiplied to obtain a perfect cube. ​

Answer 1

Answer:

Prime factorizing 243, we get,

• 243=3×3×3×3×3=3^5

.

We know, a perfect cube has multiples of 3 as powers of prime factors.

• Here, number of 3's is 5.
• So we need to multiply another 3 in the factorization to make 243 a perfect cube.

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

Answer 2

Answer:

The prime factor 3 is not a group of three. ∴ 243 is not a perfect cube. Now, 729 becomes a perfect cube. Thus, the smallest required number to multiply 243 to make it a perfect cube is 3.

243 = 3×3×3×3×3

3⁵...