Question

Find the smallest number that must be multiplied to the numbers 2,304 to obtain a perfect cube and also find the perfect cube.​

Answer 1

Answer:

6

Step-by-step explanation:

2304 = 2× 1152

= 2×2×576

= 2×2×2×288

= 2×2×2×2×144

=2×2×2×2×2×2×2×2×3×3

$= 2 {}^{3} \times 2 {}^{3} \times 2 {}^{2} \times 3 {}^{2}$

$= 4 {}^{3} \times 6 {}^{2}$

Here factor 6 is in the triplet form.It will be triplet if multiply by 6. i.e .when we multiply 2304 atleast by 6, then its factorisation will be

$2304 = 4 {}^{3} \times 6 {}^{3}$

Which is a perfect cube.

Hence the smallest number to be multiplied is 6