Question

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained.
$402$
$1989$

• A. $2,20;53,44$
• B. $12,20;53,44$
• C. $2,20;43,44$
• D. $2,20;33,44$

Answer 1

The correct option is A $2,20;53,44$

Let us try to find the square root of $402$.
$20\overline{2\mid \overline{4}\overline{02}}\mid -4\overline{40\mid 002}\underset{–}{\mid -000}\mid 2$
This shows the $(20{)}^2$ is less than $402$ by $2$. So, in order to get a perfect square, $2$ must be substracted from the given number.
$\therefore$ Required perfect square number
$=402-2=400$
Also, $\sqrt{400}=20$.
Let us try to find the square root of $1989$.
$44\overline{4\mid \overline{19}\overline{89}}\mid -16\overline{84\mid 389}\underset{–}{\mid -336}\mid 53$
This shows that $(44{)}^2$ is less than $1989$ by $53$. so, in order to get a perfect square, $53$ must be substracted from the given number.
$\therefore$ Required perfect square number
$=1989-53=1936$
Also, $\sqrt{1936}=44$.