Question

Find the least number which must be added to $6412$ so as to get a perfect square.

Also, find the square root of the perfect square so obtained.

• A. $147;81$
• B. $147;83$
• C. $149;81$
• D. $149;83$

Answer 1

The correct option is C

$149;81$

Explanation for the correct option:

We know the square of $80$ is $6400$

$6412$ is greater than $6400$.

Hence the nearest square obtained by adding a number must be greater than $80$

We find the square of the next largest number after $80$

Hence, ${81}^2=81\times 81=6561$

$6412<6561$

Hence , the closest square obtained by adding any number to $6412$ is $6561$.

The number required to be added is given by $6561-6412=149$

Hence, $149$ is the least number required to be added to $6412$ to obtain a perfect square.

The square root of this perfect square thus formed is $81$

Hence, option C is the correct answer.