Question

What is the least number that must be added to 6412 to get a perfect square?

• A. 12
• B. 120
• C. 149
• D. 161

Hint:

To find the nearest perfect square greater than a number, approximate its square root, round up, and square it. Then subtract the original number from it.

Answer 1

The Correct Option is C

We are given number = 6412 We need to find the smallest number to be added to get a perfect square. Let’s estimate the square root of 6412: \[ \sqrt{6412} \approx 79.99 \Rightarrow 79^2 = 6241, \quad 80^2 = 6400, \quad 81^2 = 6561 \] Now, \[ 6561 - 6412 = 149 \] So, if we add 149 to 6412, we get 6561 which is a perfect square: \[ 81^2 = 6561 \] Hence, the least number to be added is 149.