Question

Question 105

Solve the following question:

What is the least number, that should be subtracted from 1385 to get a perfect square? Also, find the square root of the perfect square.

Answer 1

First, find the square root of 1385 by long division method.
$\begin{array}{cc}& 37\\ 3& \overline{13}\overline{85}\\ & 9\\ 67& 485\\ & 469\\ & 16\end{array}$
Hence, the least number is 16, which should be subtracted from 1385 to get a perfect square and the required perfect square number = 1385 - 16 = 1369
$\therefore$ Square root of 1369 $=\sqrt{37\times 37}=37$