Question

By what least number should 648be multiplied to get a perfect cube? Find the new perfect cube an it's cube root

Answer 1

Hi ,

Resolving 648 into prime factors ,

we get

648 = 2 × 2 × 2 × 3 × 3 × 3 × 3

= ( 2 × 2 × 2 )×( 3 × 3 × 3 ) × 3

The Prime factor 3 does not appear

in a group of three.

So , 648 is not a perfect cube .

Hence , the smallest number by

which it is to be multiplied to make

it a perfect cube is 3 × 3 = 9.

Now ,

New perfect cube = 2³ × 3³ × 3³

= ( 2 × 3 × 3 )³

= 18³

It's cubth root = ( 18³ )^1/3

= 18^3/3

= 18

I hope this helps you.

: )

Answer 2

it is not a perfect cube

prime factorization of 648 = 2 ×2×2×3×3×3×3

(2×2×2)×(3×3×3)×3

so it is not a perfect cube