# FIND THE LEAST NUMBER TO BE ADDED TO GET A PERFECT SQUARE

## About "Find the least number to be added to get a perfect square"

Find the least number to be added to get a perfect square :

Here we are going to see how to find the least number to be added with 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 added to 1825 to make it a perfect square.

Solution :

Step 1 :

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

18, 25

When we do so, we get 18 before the comma.

Step 2 :

 Now we have to multiply a number by itself such that the product ≤ 18(The product must be greatest and also less than 18)

The above condition will be met by “4”.

Because 4 ⋅ 4  =  16  18

Now this situation is explained using long division

In the above picture, 16 is subtracted from 18 and we got the remainder 1.

Step 3 :

 Now, we have to bring down 25 and quotient 4 to be multiplied by 2. So we get 8.We don't have to continue hereafter.42 (42)  =  1764 43(43)  =  1849

The given number (1825) is > 422, but less than 432.

From this we come to know that the square root of the given number lies between 42 and 43.

1849 - 1825  =  24

Inorder to convert the given number as the square of 43, we have to add 24.

Let us look into some more examples.

Example 2 :

Find the least number, which must be added to 525 to make it a perfect square.

Solution :

 From this we come to know that the square root of the given number (525) lies between 22 and 23.222  =  484232  =  529

529 - 525 =  4

Inorder to convert the given number as the square of 23, we have to add 4.

Hence 4 is to be added to to make 525 as perfect square.

Example 3 :

Find the least number, which must be added to 1750 to make it a perfect square.

Solution :

 From this we come to know that the square root of the given number (1750) lies between 41 and 42.412  =  1681422  =  1764

1764 - 1750 =  14

Inorder to convert the given number as the square of 42, we have to add 14.

Hence 14 is to be added to to make 41750 as perfect square.

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