Question

What is the smallest number by which 2592 must be multiplied so that the product is a perfect square?

• A. 7
• B. 5
• C. 3
• D. 2

Answer 1

The correct option is D

2

$\text{Given number: 2592}\text{On prime factorising the given number,}\text{we get,}$

$\begin{array}{cc}2& 2592\\ 2& 1296\\ 2& 648\\ 2& 324\\ 2& 162\\ 3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

$2592=2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3$

$\text{By pairing the factors we get,}=(2\times 2)\times (2\times 2)\times (3\times 3)\times (3\times 3)\times 2$

$\text{Since 2 is left unpaired, we can}\text{multiply the given number by 2, such}\text{that the result will be a perfect square.}$

$\therefore \text{2 is the required number.}$