Question

Find the smallest number by which 3072 be divided so that the quotient is a perfect cube.find the sum?

Answer 1

factors of 3072 are= 2*2*2*2*2*2*2*2*2*2*3

to make a perfect cube we will divide the number by 6

Answer 2

Answer:

The smallest number by which 3072 be divided so that the quotient is a perfect cube is 6 .

And the perfect cubic number is 512 whose cubic root is 8 .

Step-by-step explanation:

Provided that:

The number is 3072; we have to divide this number with a number (The smallest one) so that the quotient will be s perfect cubic number.

Hence we are now going to factorize 3072 :

3072 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

Now calculating the cubic root of 3072 :

$3072 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 \\so \: \sqrt[3]{3072} = \sqrt[3]{2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3} \\ \: or \: \sqrt[3]{3072} = \sqrt[3]{ {2}^{3} × {2}^{3} × {2}^{3} × 2 × 3} \\ = (2 \times 2 \times 2) \times \sqrt[3]{2 \times 3} \\ = 8 \times \sqrt[3]{6}$

So if we divided 3072 by 6 we will get the perfect cubic number:

$\frac{3072}{6} = \frac{2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3}{6} \\ or \: 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 \\ \\ so \: \sqrt[3]{512} = \sqrt[3]{ {2}^{3} \times {2}^{3} \times {2}^{3} } \\ = 2 \times 2 \times 2 \\ = 8$

And the perfect cubic number is 512 whose cubic root is 8 .