Question

Find the least number which must be added to each of the following numbers so as to get a perfect square:
(i) $525$ (ii) $1750$ (iii) $252$ (iv) $1825$ (v) $6412$

Answer 1

(i) $525$

We know that ${22}^2=484$ and ${23}^2=529$

So, we need to add $529-525=4$ to $525$ to get a perfect square.

(ii) $1750$

We know that ${41}^2=1681$ and ${42}^2=1764$

So, we need to add $1764-1750=14$ to $1750$ to get a perfect square.

(iii) $252$

We know that ${15}^2=225$ and ${16}^2=256$

So, we need to add $256-252=4$ to $252$ to get a perfect square.

(iv) $1825$

We know that ${42}^2=1764$ and ${43}^2=1849$

So, we need to add $1849-1825=24$ to $1825$ to get a perfect square

(v) $6412$

We know that ${80}^2=6400$ and ${81}^2=6561$

So,we need to add $6561-6412=149$ to $6412$ to get a perfect square