Find the smallest number which must be subtracted from 63535 to make it a perfect square.

Correct option is B

Given:

We need to find the smallest number that must be subtracted from 63535 to make it a perfect square.

Concept Used

A perfect square is an integer that is the square of another integer. To find the smallest number to subtract from 63535 to make it a perfect square, we can:
Find the nearest integer whose square is just less than 63535.
Subtract that square from 63535 to determine the required difference.

Solution

Take the square root of 63535 to find the nearest integer whose square is less than 63535.

The integer part of $$\sqrt{63535}$$​ is approximately:
​$$\text{Integer part of } \sqrt{63535} = 252$$​​

Calculate the square of this integer:

​$$252^2 = 63504$$​​Subtract this square from 63535 to find the difference:

63535 - 63504 = 31

The smallest number that must be subtracted from 63535 to make it a perfect square is 31