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**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 s

**quare of numbers ending with 6**, then we have to add the doubled the number to the square..
Examples:

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

ReplyDeleteThis method also useful for ending numbers with 1 or 9..

ReplyDeleteEx 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

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

Deletethank u prasad

DeletePlus symbol not displyed in the last comment..

ReplyDelete40*2+1=81

1600+81=1681

12 2 = 144 {(12 * 1(first digit * number) =12 + (first digit * second digit) = 1*2 = 2 +last digit square 22 = 4}

ReplyDelete=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

12 ^2 = 144 {(12 * 1(first digit * number) =12 + (first digit * second digit) = 1*2 = 2 +last digit square 22 = 4}

ReplyDelete=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

Thank you so much brother..

Deletethe best shortcut method for square any digit is a^2 *2ab* b^2

ReplyDeletecan you plz explain for the above technique for 56^2..

ReplyDelete55^2=3025

ReplyDelete56*2=112

112+1=113

3025+113=3138 but actual answer is 3136.. am I correct??

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

Deleteok got it.. thank you.

Deletegr8.........

ReplyDelete