Finding Nearest Perfect Square by Subtraction
Finding Nearest Perfect Square by Subtraction
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. Subtract the remainder from the given number. Now the given number becomes a perfect square.
Illustration 1: Find the least number which must be subtracted from 18265 to make it a perfect square. Also, find the square root of the resulting number.
Solution: Let us work out the process of finding the square root of 18265 by the long division method.
We find that in the process of working out the square root of 18265 by the long division method, the remainder in the last step is 40 . This means that if 40 be subtracted from the given number, the remainder will be zero and the new number will be a perfect square.
Hence, the required least number = 40
and, requried square number = 18265 - 40 = 18225
So, which is a perfect square.
Illustration 2: Find the greatest number of six digits which is a perfect square.
Solution: We know that the greatest number of six digits is 999999. In order to find the greatest number of six digits which is a perfect square, we must first find the smallest number that must be subtracted from 999999 to make it a perfect square. For this, we work out the process of finding the square root of 999999 by the long division method as given below.
Which is the greatest three-digit perfect square ? | |||
| Right Option : B | |||
| View Explanation | |||
Which least number should be subtracted from 629 so as to get a perfect square ? | |||
| Right Option : A | |||
| View Explanation | |||
Find the least number which must be subtracted from 1448 to make it a perfect square. | |||
| Right Option : C | |||
| View Explanation | |||
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