Finding Nearest Perfect Square by Addition
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
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It is evident from the above work that
Also 306452 is (4416 - 3952) = 464 less than .
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.
Which is the smallest 4 - digit perfect sqaure ? | |||
| Right Option : A | |||
| View Explanation | |||
Find the least number which must be added to 506900 to make it a perfect square. | |||
| Right Option : C | |||
| View Explanation | |||
What must be added to 29518 to make it a perfect square? | |||
| Right Option : D | |||
| View Explanation | |||
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