Question

Find the least number which must be subtracted from each of the following so as to get a perfect square. Also find the square root of the perfect square so obtained.
$\left(i\right)402$ $\left(ii\right)1989$ $\left(iii\right)3250$ $\left(iv\right)825$ $\left(v\right)4000$

Answer 1

In order to find the least number to be subtracted from the given no.,

we must find a smaller perfect square number, closest to the given number.

i) $402$

The closest smaller perfect square number is $400$

Difference $=402-400=2$

Hence, $2$ must be subtracted from $402$ in order to make it a perfect square.

$\therefore \sqrt{400}=20$

ii) $1989$

The closest smaller perfect square number is $1936$.

Difference $=1989-1936=53$

Hence, $53$ must be subtracted from $1989$ in order to make it a perfect square.

$\therefore \sqrt{1936}=44$

iii) $3250$

The closest smaller perfect square number is $3249$.

Difference $=3250-3249=1$

Hence, $1$ must be subtracted from $3250$ in order to make it a perfect square.

$\therefore \sqrt{3249}=57$

iv) $825$

The closest smaller perfect square number is $784$.

Difference $=825-784=41$

Hence, $41$ must be subtracted from $825$ in order to make it a perfect square.

$\therefore \sqrt{784}=28$

v) $4000$

The closest smaller perfect square number is $3969$.

Difference $=4000-3969=31$

Hence, $31$ must be subtracted from $4000$ in order to make it a perfect square.

$\therefore \sqrt{3969}=63$