# A Simple Technique for Squaring of Numbers ending with 4 and 6

Friends, in the previous post we had discussed the technique of squaring numbers ending with 9 and 1. In this post, we will discuss how to find the squares of the numbers ending with 4 and 1. First of all let me clear you guts one thing, to be perfect in this method, you should be perfect with addition and subtraction. And the secret in getting this trick look easiest is: Practice, practice and practice… Before entering into the concept, let us take a deeper look at the squares of numbers.
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25

The difference between the squares of the numbers are 3, 5, 7, 9 respectively.. That is, the difference between two successive squares is an ODD NUMBER. So that we have come to know the secret, let us think how to know what will be the odd number that we have to subtract or add?! Let us consider 4^2 =16; 5^2 = 25, the difference between them is 9. Now, how to remember the difference.. it’s very simple:
Let us take an example, we have to find the square of 14.
Step – 1: Nearest number ending with 5 is 15, 15^2 = 225
Step – 2: 15*2 = 30, now, 30 – 1 = 29
Step – 3: 225 – 29 = 196 --> 14^2
NOTE:
(i)    We usually use this method to find the squares of numbers ending with 4 and 6 because, it’s pretty simple to get the square of a number ending with 5.
(ii)    When we are finding the square of numbers ending with 6, then we have to add the doubled the number to the square..
Examples:
1)    26^2 =?
Sol: 25^2 = 625; 25*2 = 50--> 50 + 1 =49
Hence, 26^2 = 625 + 51 = 676
2)    54^2 =?
Sol: 55^2 = 3025; 55*2 = 110--> 110 – 1 = 109
Hence, 54^2 = 3025 – 109 = 2916
3)    96^2 =?
Sol: 95^2 = 9025; 95*2 = 190 --> 190 + 1 = 191
Hence, 96^2 = 9025+191 = 9216
4)    114^2 =?
Sol: 115^2 = 13225; 115*2 = 230 --> 230 – 1 = 229
Hence, 114^2 = 13225 – 229 = 12996

SQUARES OF NUMBERS ENDING WITH 5
The main root for doing the above process is to find the squares of the numbers ending with 5. We know that the square of a number ending with 5 will always end in 5. i.e., X5^2 = YYY5! Right? Let us give this another shot, the last two digits of the square of a number ending with 5 will always be “25”.
Examples:
1)    25^2 =?
Sol:   Step 1: The last two digits will be 25
Step 2: The ten’s digit of the given number is: 2. Now, 2 8 (2+1) = 6
Step 3: hence the answer is: 25^2 = 625
2)    65^2 =?
Sol: 6*(6+1) = 42 --> 65^2 = 4225
3)    125^2 =?
Sol: 12*(12+1) = 156 --> 125^2 = 15625
4)    45^2 =?
Sol: 4*(4+1) = 20 --> 45^2 = 2025
5)    95^2 =?
Sol: 9*(9+1) = 90 --> 95^2 = 9025

Thanks to Hareesh Kumar for sharing such a nice technique

1. Very Useful....But.,had this been posted earlier, it might have been easier for us for these exams.

2. This method also useful for ending numbers with 1 or 9..
Ex for 41^2:
nearest number ending with 0 is 40..
Step 1:40^2=1600
step 2:40*2 1=81
step 3:41^2=1600 81=1681

Ex for 39^2:
1:40^2=1600
2:40*2-1=79
3:39^2=1600-79=1521

1. Thank you friend.. The method is already available: http://www.gr8ambitionz.com/2013/12/shortcut-squaring-techniques.html

3. Plus symbol not displyed in the last comment..
40*2+1=81
1600+81=1681

4. 12 2 = 144 {(12 * 1(first digit * number) =12 + (first digit * second digit) = 1*2 = 2 +last digit square 22 = 4}
=12+2 =14
= 22=4
First we have to write last digit by squaring and then do (first digit * number) + (first digit * second digit) gives remaining digits
Note : If the square of last digit exceeds 10 write last digit of square and add remaining digits to the total
132 =169 { (13*1=13)+(1*3)=3} =16 last digit square =9 } =169

This will be applicable to 1-99 squares

5. 12 ^2 = 144 {(12 * 1(first digit * number) =12 + (first digit * second digit) = 1*2 = 2 +last digit square 22 = 4}
=12+2 =14
= 22=4
First we have to write last digit by squaring and then do (first digit * number) + (first digit * second digit) gives remaining digits
Note: If the square of last digit exceeds 10 write last digit of square and add remaining digits to the total
13^2 =169 { (13*1=13)+(1*3)=3} =16 last digit square =9 } =169

This will be applicable to 1-99 squares

1. Thank you so much brother..

6. the best shortcut method for square any digit is a^2 *2ab* b^2

7. can you plz explain for the above technique for 56^2..

8. 55^2=3025
56*2=112
112+1=113
3025+113=3138 but actual answer is 3136.. am I correct??

1. Friend, it is 55*2 = 110; 110+1 = 111 ==> 3025+111 = 3136

2. ok got it.. thank you.

9. gr8.........