Sita has 392 unit cubes. The prime factorisation of 392 is $2^{3} \times 7^{2}$ .
By what smallest number must 392 be multiplied so that the product is a perfect cube?

Question

Sita has 392 unit cubes. The prime factorisation of 392 is 2^3 x 7^2. By what smallest number must 392 be multiplied so that the product is a perfect cube?

Accepted Answer

7. 392 = 2^3 x 7^2. The 7s are one short of a triple, so multiply by 7: 392 x 7 = 2744 = 2^3 x 7^3 = 14^3, a perfect cube.

Sita has 392 unit cubes. The prime factorisation of 392 is $2^{3} \times 7^{2}$ .
By what smallest number must 392 be multiplied so that the product is a perfect cube?

Step-by-Step Solution

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More Class 8 Cube Root by Prime Factorisation practice

Sita has 392 unit cubes. The prime factorisation of 392 is 23×72.By what smallest number must 392 be multiplied so that the product is a perfect cube?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Cube Root by Prime Factorisation practice

Sita has 392 unit cubes. The prime factorisation of 392 is $2^{3} \times 7^{2}$ .
By what smallest number must 392 be multiplied so that the product is a perfect cube?