Question

find the least number which when multiplied with 16785 gives the product a perfect cube find the cube root of the product thus obtained​

Answer 1

Answer:

Prime factorising 3600, we get,

3600=3×3×2×2×2×2×5×5

=3

2

×2

4

×5

2

.

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

i.e. here, the number has to be multiplied by 3×2

2

×5=60 to make it a perfect cube.

Therefore, the new number =3600×60=216000.

Then,

3

216000

=

3

3

3

×2

6

×5

3

=3×2

2

×5=60.