Question

find the smallest natural number by which 6860 should be multiplied so as to get a perfect square ​

Answer 1

Answer:

5

Prime factorising 68600, we get,

68600=2×2×2×5×5×7×7×7

=2

3

×5

2

×7

3

.

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

Here, number of 2's is 3, number of 5's is 2 and number of 7's is 3.

So we need to multiply another 5 in the factorization to make 68600 a perfect cube.

Hence, the smallest number by which 68600 must be multiplied to obtain a perfect cube is 5.