Question

Is 2352 a perfect square? If not, find the smallest multiple of 2352 which is a perfect square. Find the square root of the new number. [4 MARKS]

Answer 1

Concept : 1 Mark
Prime factorisation : 2 Marks
Conclusion : 1 Mark

$\begin{array}{cc}2& 2352\\ 2& 1176\\ 2& 588\\ 2& 294\\ 3& 147\\ 7& 49\\ & 7\end{array}$

$2352=2\times 2\times 2\times 2\times 3\times 7\times 7$

As the prime factor 3 has no pair, 2352 is not a perfect square.

If 3 gets a pair then the number will become perfect square.

So, we multiply 2352 by 3 to get,

$2352\times 3=2\times 2\times 2\times 2\times 3\times 3\times 7\times 7$

$\therefore 2352\times 3=7056$ is a perfect square.

Thus, the required smallest multiple of 2352 is 7056 which is a perfect square.

$\sqrt{7056}=2\times 2\times 3\times 7=84$