**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 > 42^{2}, but less than 43^{2}.

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. 22 23 |

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. 41 42 |

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.

- How to find the number of digits of square root of a number
- Find the least number to be added to get a perfect square
- How to find the least number to be subtracted to get a perfect square
- Find the least number should be multiplied to get a perfect square
- Find the least number should be divided to get a perfect square

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