## How to find the square of a two digit number easily

**Square Means :** When any number is multiplied by itself , it is called as the square of a number

a) Square plays very important role in mathematics.

b) For doing the square of any two digit number having number of shortcuts are there out of that I suggested you one of the best and easy trick for square

c) First of all I suggest you must remember squares of first 30 numbers. Upto 20 numbers most of the students already know so remaining number means upto 30, it is very easy to remember. It will also very much helpful to do square of 3 digit numbers.

d) After 30 you do not need to worry about that. You just following the process than you will able to do square of reaming 2 digit numbers.

Number |
Square |
Number |
Square |
Number |
Square |

1 | 1 | 11 | 121 | 21 | 441 |

2 | 4 | 12 | 144 | 22 | 484 |

3 | 9 | 13 | 169 | 23 | 529 |

4 | 16 | 14 | 196 | 24 | 576 |

5 | 25 | 15 | 225 | 25 | 625 |

6 | 36 | 16 | 256 | 26 | 676 |

7 | 49 | 17 | 289 | 27 | 729 |

8 | 64 | 18 | 324 | 28 | 784 |

9 | 81 | 19 | 361 | 29 | 841 |

10 | 100 | 20 | 400 | 30 | 900 |

### Square of a number from 31 to 80 :

Here you must remember the following the steps ( Note : Friends do not afraid for following steps it is very easy for better understanding purpose I mentioned here )

a) The answer having two parts and each part required for 2digits only. (except only for 31, here came one digit for 2nd part) .

b) Take number a “X” than 50 subtract from that number i.e X -50

c) For 1st part you square of that value i.e (X-50)2

d) In first part required 2 digits so if it came less than two digits than add “0” for second place otherwise if it came more than 2 digits than 3rd digit should be carryover the next part i.e 2nd part.

e) For Second part purpose our base number is 25. i.e the value X-50 is to be add to 25 and also to be add for this if any carry over number from 1st part.

**Let us go through the examples.**

**Example No. 1** : ** 43 ^{2}**

Step 1 : 43-50 = -7

Step 2 : (-7)^{2} = 49. Our 1st part** 49.**

Step 3 : 25+ (-7) + 0(No carry over from 1st part) = 18. Our 2nd part is **18**.

So our final answer is **1849**

**Example No. 2** : ** 48 ^{2}**

Step 1 : 48-50 = -2

Step 2 : (-2)^{2} = 4 Our 1st part** 04 **(Require 2digits in 1st part).

Step 3 : 25+ (-2) + 0(No carry over from 1st part) = 23. Our 2nd part is **23**.

So our final answer is **2304**

**Example No.3** : ** 67 ^{2}**

Step 1 : 67-50 = +17

Step 2 : (17)^{2} = 289 Our 1st part** 89 **(Require 2digits in 1st part and “2” carryover to 2nd part.)**.**

Step 3 : 25+ (+17) + 2(it is carry over from 1st part) = 44. Our 2nd part is **44**.

So our final answer is **4489**

### Square of a number from 81 to 99 :

Here you must remember the following the steps

a) The answer having two parts and each part required for 2digits only.

b) Take number a “X” than 100 subtract from that number i.e X -100

c) For 1st part you square of that value i.e (X-100)2

d) In first part required 2 digits so if it came less than two digits than add “0” for second place otherwise if it came more than 2 digits than 3rd digit should be carryover the next part i.e 2nd part.

e) For Second part purpose our base number is X . i.e the value X-100 is to be add to X and also to be add for this if any carry over number from 1st part.

**Example No.4** : ** 86 ^{2}**

Step 1 : 86-100 = -14

Step 2 : (-14)^{2} = 196 Our 1st part is **96 **(Require 2digits in 1st part so remaining value “1” is carryover to 2nd part.)**.**

Step 3 : 86 + (-14) + 1(it is carry over from 1st part) = 73. Our 2nd part is **73**.

So our final answer is **7396.**

**Example No.5** : ** 97 ^{2}**

Step 1 : 97-100 = -3

Step 2 : (-3)^{2} = 9 Our 1st part is **09 **(Require 2digits in 1st part)**.**

Step 3 : 97 + (-3) + 0(it is carry over from 1st part) = 94. Our 2nd part is **94**.

So our final answer is **9409.**

Friends definitely I can tell while you are doing the practice the above shortcut way than you can definitely do square of two digit number in fraction of section.

Friends in this blog explained about easy methods for all types of mathematics sums

Hi friends Thanks for reading. I Hope you liked it. Give feed back, comments and please don’t forget to share it.

## 6 thoughts on “Easiest way to find square of a 2 digit number | Shortcut trick for Square”

## chetan

(April 6, 2018 - 3:05 pm)Nice trick

## sivaalluri

(April 11, 2018 - 5:04 pm)Thank you Mr.Chetan

## Yasir Qadhi

(July 23, 2018 - 9:44 am)can u use this to find the last digit of any power.

lets say 2017^2017

## sivaalluri

(July 25, 2018 - 2:16 pm)Finding the last digit of an expression purpose simply find the remainder of that expression divided by 10. In the same way for finding the last two digits of an expression purpose find the remainder of that expression divided by 100.

Now according to yous question last digit of the expression 2017

^{2017}So last digit of the number 2017

^{2017}is 7## square shortcut

(September 28, 2018 - 11:35 am)hi siva

Actually the method you have given is very good for finding square of a number. when am searching about this topic I found your blog. looks nice

## devendra

(April 26, 2019 - 12:16 pm)hello shiva sir. very nice trick. please give me trick for 5digit, 6digit, 7digit… up to 15digit multiplication tricks & division tricks.