Question

9. Find the smallest number by which each of the following numbers must be divided so that
is a perfect cube. Also, find the cube root of the quotient.
(1) 3584
(ii) 1458
(ii) 120393​

Answer 1

Answer:

1) 3584=2×2×2×2×2×2×2×3×11

in the prime factorization of 3584 2,3,11 are not

in triplet

so, it is not a perfect cube number

so, the required smallest number is 2×3×11=66

and cube root of 3584is =2×2×2×3×11=264

Answer 2

We take lcm of 120393.

120393 = 3 \times 3 \times 3 \times 7 \times 7 \times 7 \times 13

120393 = 3 \times 3 \times 3 \times 7 \times 7 \times 7 \times 13

Here, 13 is unpaired.

So we divide 120393 by 13

The we get is 9261 which is a perfect cube.

9261= 21*21*21

Therefore 21 is cube root of 9261.

Hope this helps.