Question

What is the smallest number by which 13500 must be divided so that the quotient is

a perfect cube? Also, find the cube root of the quotient.​

Answer 1

13500 = 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5

= 2² x 3³ x 5³

=> If we multiply by 2, we get a perfect cube.

=> Dividing 13500 by 1/2 will give quotient 27000 which is perfect cube.

It may not be possible to find smallest number. Another solution smaller than 1/2 is 1/(2⁴ x 3³ x 5³)

Note : Smallest number does not mean only integers.

Alternatively, divide 13500 by 4 to get 3375 which is a perfect cube !!!!

It all depends how you interpret “Number”.

and the cube root of 27000 is 30

hope this answer helps you

Answer 2

Answer:

To Find:-

13500 is a perfect cube or not?

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Solution:-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

By Prime Factorisarion Method

$\tt{2} \: \: \: | \tt\pink{\: \: 13500 \: \: }$

$\tt{2} \: \: \: | \tt\pink{\: \: 6750 \: \: }$

$\tt{3} \: \: \: | \tt\pink{\: \: 3375\: \: }$

$\tt{3} \: \: \: | \tt\pink{\: \: 1125\: \: }$

$\tt{3} \: \: \: | \tt\pink{\: \: 375\: \: }$

$\tt{5} \: \: \: | \tt\pink{\: \: 125\: \: }$

$\tt{5} \: \: \: | \tt\pink{\: \: 25\: \: }$

$\tt{5}\: \: \: | \tt\pink{\: \: 5\: \: }$

$\: \: \: \: \: | \tt\pink{\: \: \: 1\: \: }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\tt{ \sqrt[3]{13500} } = \tt \pink{\sqrt[3]{2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt \pink{ {2}^{2} \times {3}^{3} \times {5}^{3} }$

No, 13500 is not a perfect cube.

The least number multiplied to make 13500 a perfect square is 2 × 2 = 4