# HOW TO FIND THE LEAST NUMBER TO BE SUBTRACTED TO GET A PERFECT SQUARE

## About "How to find the least number to be subtracted to get a perfect square"

How to find the least number to be subtracted to get a perfect square :

Here we are going to see how to find the least number to be  the given number to get a perfect square.

For this, we use the method called long division.

Let us see an example to understand the concept.

Example 1 :

Find the least number which must be subtracted from 1989 so as to get a perfect square

Solution :

Step 1 :

Separate the digits by taking commas from right to left once in two digits.

19, 89

When we do so, we get 19 before the comma.

Step 2 :

 Now we have to multiply a number by itself such that the product ≤ 4(The product must be greatest and also less than 19)

The above condition will be met by “4”.

Because 4 4  =  16

Now this situation is explained using long division

In the above picture, 16 is subtracted from 19 and we got the remainder 3.

Step 3 :

 Now, we have to bring down 89 and quotient 4 to be multiplied by 2. So we get 8.By multiplying 4 and 84 we get 336.If we subtract 336 from 389, we get 53.

We don't have to continue hereafter.

44 (44)  =  1936

If we subtract 53 from 1989, we get 1936 which is the perfect square.

Hence 53 is the least number to be subtracted from the given number (1989) to get a perfect square.

Example 2 :

Find the least number, which must be subtracted from 3250 to make it a perfect square.

Solution :

 From this we come to know that the square root of the given number (3250) is greater than 572572  =  32493250 - 3249  =  1

Inorder to convert the given number as the square of 57, we have to subtract 1.

Hence 1 is the least number to be subtracted from 3250 to get a perfect square.

Example 3 :

Find the least number, which must be subtracted from 4000 to make it a perfect square.

Solution :

 From this we come to know that the square root of the given number (4000) is greater than 632632  =  3969

4000 - 3969  =  31

Inorder to convert the given number as the square of 63, we have to subtract 31.

Hence 31 is the least number to be subtracted from 4000 to get a perfect square.

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