Question

What is the smallest number by which $3645$ be multiplied so that the product becomes a perfect cube?

• A. $5$
• B. $25$
• C. $15$
• D. $35$

Answer 1

The correct option is B $25$

Let us factorize the number 3645 .

$\Rightarrow 3645=5\times 9\times 9\times 9$

For a number to be a perfect cube , all the numbers should have triplets .

Here only 9 has a triplet . And 5 is 2 two times short of a triplet . Hence we multiply $5\times 5$ both the sides.

$\Rightarrow 3645\times 5\times 5=5\times \times 5\times 5\times 9\times 9\times 9$

Hence the smallest number by which 3645 must be multiplied to get a perfect cube is $25$