**Properties of square numbers are:**

- If a number has 0, 1, 4, 5, 6 or 9 in the unit’s place, then it may or may not be a square number. If a number has 2, 3, 7 or 8 in its units place then it is not a square number.
- If a number has 1 or 9 in unit’s place, then it’s square ends in 1.
- If a square number ends in 6, the number whose square it is, will have either 4 or 6 in unit’s place.

**Square Root of a Number **

Finding the number** whose square is known **is known as finding the **square root**. Finding square root is **inverse operation** of finding the square of a number.

**Estimating Square Roots**

Estimating the square root of 247:

Since:

i.e.

But it is not very close.

Also, and

256 is much closer to 247 than 225.

Therefore, is approximately equal to 16.

**Numbers between Square Numbers**

There are **2n** non-perfect square numbers between squares of the numbers *n* and (*n* + 1), where *n *is any natural number.

Example:

- There are two non-perfect square numbers (2, 3) between 1
^{2}=1 and 2^{2 }= 4. - There are four non-perfect square numbers (5, 6, 7, 8) between 2
^{2}= 4 and 3^{2}=9.

**Pythagorean Triplets**

2m, (m^{2}−1) and (m^{2}+1) forms a Pythagorean triplet.

For m = 2, 2m = 4, m^{2}−1 = 3 and m^{2}+1 = 5.

So, 3, 4, 5 is the required Pythagorean triplet.

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