Finding Nearest Perfect Square by Addition


 
 
Concept Explanation
 

Finding Nearest Perfect Square by Addition

To find the least number which must be subtracted to a given number to make it a perfect square, the steps are as follows:

1. Start finding the square root of the given number by using the long division method.

2. Find the remainder at the last step of division.

3. Now add 1 to the divisor.

4. The new remainder will be with a negative sign. or we can say we will the excess in the remainder.

5. Add the excess number obtained to the given number.

6. Now the new number will be a perfect square.

Illustration 1: Find the least number which must be added to 306452 to make it a perfect square.

Solution: Let us first work out the process of finding the square root by the division method

                                                  

It is evident from the above work that (553)^{2}<306452<(554)^{2}.

Also 306452 is (4416 - 3952) = 464 less than (554)^{2}.

Thus, if we add 464 to 306452, it will be a perfect square.

Hence, the required least number is 464

Illustration 2: Find the least number of four digits which is a perfect square.

Solution: We know that the least number of 4 digits is 1000.

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Sample Questions
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Question : 1

Which is the smallest 4 - digit perfect sqaure ? 

Right Option : A
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Explanation
Question : 2

Find the least number which must be added to 506900 to make it a perfect square.

Right Option : C
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Explanation
Question : 3

What must be added to 29518 to make it a perfect square?

Right Option : D
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Explanation
 
 


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