**Square of a Number**

When a number is multiplied by itself we can say that number is a squared. It is denoted by a number raised to the power 2. In general x is any number then *x ^{2}= x multiplied with x. *x

^{2}represents square of x.

For Example: 4

^{2 }

It means 4 is multiplied by 4 and this is equal to 16

We can say we squared 4 and we got 16. 4

^{2}is read as 4 raise to power 2 or 4 squared.

Note: If we have a negative number then always square of negative number is positive

For example: (-4)

^{2}= 16

Why its +16?

Because square is but that is basically number multiplied by itself right?

So if we multiply -4X-4= +16

Negative sign multiply by negative sign then result is positive that is multiplication rule.

**Perfect Square**

A number is called a perfect square if it is a square of number.

For example:

16= 4

^{2}

64=8

^{2}

Fast calculation of square for exam

You need to learn mostly till 30.

Number | Square | Number | Square |

1 | 1 | 16 | 256 |

2 | 4 | 17 | 289 |

3 | 9 | 18 | 324 |

4 | 16 | 19 | 361 |

5 | 25 | 20 | 400 |

6 | 36 | 21 | 441 |

7 | 49 | 22 | 484 |

8 | 64 | 23 | 529 |

9 | 81 | 24 | 576 |

10 | 100 | 25 | 625 |

11 | 121 | 26 | 676 |

12 | 144 | 27 | 729 |

13 | 169 | 28 | 784 |

14 | 196 | 29 | 841 |

15 | 225 | 30 | 900 |

Shortcut trick to find out the Square of numbers if its end with 5

For example if number is 25^{2} = 6__25 __

Last two digits are Square of 5 that is 25.

For first digit add 1 to the first digit of that number like

2+1=3

And now multiply this result with first number

3X2= 6.

Combine both 6 and 25 then you will get 625.

**SQUARE ROOT**

That is opposite of square. The square root of a number is that number which is multiplied by itself gives us the given number.

In general, if x is square root of y then

x=√y implies x^{2}=y

As we know square of 4 is 16. So 4 is known as square root of 16. Square root is denoted by symbol “√ “.

Thus Square root of 16 is

√16= 4

Note: a square cannot be a negative number. It is always be positive. The square of negative number as well as positive number has to be positive. So the square root of any number has two values – Negative and Positive.

**Square root with factorization**

Steps to find the square & square root of Numbers by Factorization.

Express the given number as a product of prime factor.

Make pair of similar factors.

The product of prime factor, after taking one factor out of every pair will give the square root of the number.

Lets us take an example

Q1 : Find out the square root of 144.

Solution: √144= √__2X2__X__2X2__X__3X3__

=2X2x3

=12

So √144=12.

Explanation given below:

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