**How to check whether the given number is perfect square or not ?**

Here we are going to see How to check whether the given number is perfect square or not.

**Perfect Square :**

The numbers 1, 4, 9, 16, 25, g are called perfect squares or square numbers as

1 = 1^{2}, 4 = 2^{2}, 9 = 3^{2}, 16 = 4^{2} and so on.

A number is called a perfect square if it is expressed as the square of a number.

We may observe the following properties through the patterns of square numbers.

**Property 1 :**

In square numbers, the digits at the unit’s place are always 0, 1, 4, 5, 6 or 9. The numbers having 2, 3, 7 or 8 at its units' place are not perfect square numbers.

**Property 2 :**

(i) If a number has 1 or 9 in the unit's place then its square ends in 1.

Number 1 9 11 |
Square 1 81 121 |

(ii) If a number has 2 or 8 in the unit's place then its square ends in 4.

Number 2 8 12 |
Square 4 64 144 |

(iii) If a number has 3 or 7 in the unit's place then its square ends in 9.

Number 3 7 13 |
Square 9 49 169 |

(iv) If a number has 4 or 6 in the unit's place then its square ends in 6.

Number 4 6 14 |
Square 16 36 196 |

(v) If a number has 5 in the unit's place then its square ends in 5.

Number 5 15 25 |
Square 25 225 625 |

(v) If a number has 5 in the unit's place then its square ends in 5.

Number 5 15 25 |
Square 25 225 625 |

**Property 3 :**

When a number ends with ‘0’ , its square ends with double zeros.

Let us consider the following examples,

10^{2} = 100, 20^{2} = 400

100^{2} = 10000, 200^{2} = 40000

**Property 4 :**

If a number ends with odd number of zeros then it is not a perfect square.

Let us consider the examples,

Check if 100 is a perfect square.

100 is a perfect square. Because it has even number of zeroes.

100 = 10 ⋅ 10 = 10^{2}

(ii) 81000 = 81 ⋅ 10 ⋅ 100

= 9^{2}⋅ 10 ⋅ 10^{2}

Hence 81000 is not a perfect square. Because it has odd number of zeroes.

**Property 5 :**

(i) Squares of even numbers are even.

(ii) Squares of odd numbers are odd.

Let us look into some example problems to understand the above concepts.

**Example 1 :**

By observing the unit’s digits, which of the numbers 3136, 867 and 4413 can not be perfect squares?

**Solution :**

Since 6 is in units place of 3136, there is a chance that it is a perfect square.

867 and 4413 are surely not perfect squares as 7 and 3 are the unit digit of these numbers.

**Example 2 :**

Just observe the unit digit and state if the given number is perfect square or not.

9348

**Solution :**

In square numbers, the digits at the unit’s place are always 0, 1, 4, 5, 6 or 9.

Since the unit digit is 8, it is not a perfect square.

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