Question

For $2028$ 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.
[4 marks]
[NCERT - Ex 6.3, Q5 (iv)]
[Finding Square Root]

Answer 1

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

$2028=2\times 2\times 3\times 13\times 13$
[2 mark]

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

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

Thus, $78$ is the square root of the square number so obtained.
[1 mark]