Question

Is 1188 a perfect cube? If not by which smallest natural number should 1188 be divided so that the quotient is a perfect cube?
Is 68600 a perfect cube? If not find the smallest number by which 68600 must be multiplied to get a perfect cube.​

Answer 1

Answer:

Prime factorising 1188, we get,

1188=2×2×3×3×3×11

=2

2

×3

3

×11.

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

Here, number of 2's is 2, number of 3's is 3 and number of 11's is 1.

So we need to divide 2

2

and 11 from the factorization to make 1188 a perfect cube.

Hence, the smallest number by which 1188 must be divided to obtain a perfect cube is 2

2

×11=44