Question

Question 5 (iv)

For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained:

2028

Answer 1

$2028=2\times 2\times 3\times 13\times 13$

Here, prime factor 3 has no pair. Therefore 2028 must be multiplied by 3 to make it a perfect square.

$\therefore 2028\times 3=6084$
And $\sqrt{6084}=2\times 2\times 3\times 3\times 13\times 13=78$

$\begin{array}{cc}2& 2028\\ 2& 1014\\ 3& 507\\ 13& 169\\ 13& 13\\ & 1\end{array}$