Question

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square:
(i) $402$ (ii) $1989$ (iii) $3250$ (iv) $825$ (v) $4000$

Answer 1

$\left(i\right)402$

We know that ${20}^2=400$ and ${21}^2=441$

So, we need to subtract $402-400=2$ from $402$ to get a perfect square

$\left(ii\right)1989$

We know that ${44}^2=1936$ and ${45}^2=2025$

So, we need to subtract $1989-1936=53$ from $1989$ to get a perfect square

$\left(iii\right)3250$

We know that ${57}^2=3249$ and ${58}^2=3364$

So, we need to subtract $3250-3249=1$ from $3250$ to get a perfect square

$\left(iv\right)825$

We know that ${28}^2=784$ and ${29}^2=841$

So, we need to subtract $825-784=41$ from $825$ to get a perfect square

$\left(v\right)4000$

We know that ${63}^2=3969$ and ${64}^2=4096$

So, we need to subtract $4000-3969=31$ from $4000$ to get a perfect square