Many readers have requested me to teach them a simple method to square two and three digit numbers. In bank exams calculation speed is very crucial. So today I have decided to explain my Squaring technique.

## Technique

In case of two digit number deduct last digit and add it to another number and then add square of same.

In this technique we simplify the squaring method by making one unit's digit zero. It is far easy to multiply 50*24 than 54*24. So I used this technique. Try practice more to become expert in this technique.

## Let's take some examples

Find square of 53.

=(53*53)

= (53+3) * (53-3) + (3*3)

=(56*50) + 9

= (560*5) + 9

= 2800 + 9 = 2809

Let's take another example

Find square of 69

= (69*69)

= (69+1) * (69-1) + (1*1)

= (70*68) + 1

= (680*7) + 1

= 4761

Let's take one more example

Find square of 45

= (45*45)

= (45-5)*(45+5) + (5*5)

= (40*50) + 25

= 2000+25

= 2025

Comment below in case you find any problem in this technique.

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hello sir....in 53 square u have taken 3*3 and in 69 square u have taken 1*1....can u tell me y u have taken and the trick?

ReplyDelete=69*69

Delete=(69-9)*(69+9)+(9*9)

=60*78+81

=(780*6)+81

=4680+81

=4761

(a^2 - b^2) = (a+b)(a-b)

Deletea^2= (a+b)(a-b) + b^2

thanku sir.... :) ur website is very helpful .

ReplyDeletehi

Deletehow find this study material

Yes use same technique

ReplyDeletesir how to square more then 2 digits no?same techcnique will be implemented or not?

ReplyDeletevery good technique thanks sir

ReplyDeleteHello Sir, You are doing very good :)

ReplyDeletehow to multiply with which no. how it will come to know

ReplyDeleteWow, its really fantastic technique. .By using like this techniques we can surely increase our mathematical speed in any competitive exms. .thank you

ReplyDeletewhy u r using 1 instead of 9 while squaring 69

ReplyDeleteyou can use 9 also but its easy to use 1. Main idea is to come to tens digit by whatever addition or subtraction.

DeleteSir is it necessary to mug up the sqiare roots till 30.

ReplyDeleteYes, it is required

DeleteNice technique....

ReplyDeleteI know other technique bt from 26 to 75 squares for that 1 should know squares of 1 to 25, which i feel is better than this technique bcoz u dont need to multiply any but v should do addition. I'm taking the same examples given here

ReplyDelete53 square = 2500+(100*number more than 50)+square of the increased number

i.e

IF THE NUMBER IS MORE THAN 50 DO SQUARES AS BELOW

Square of 53 = 2500 + 300 + 9 = 2809

Square of 69 = 2500 + 1900 + 361 = 4761

NOW IF THE NUMBER IS BELOW 50, DO AS BELOW

Square of 45 = 2500 - 500 + 25 = 2025

Thanks for your contribution.

DeleteYour trick is really good. But while finding square of 83, I found it really long.

Square between 75-100

ReplyDelete1.assume ,we have to find the square of N.first find the differencecwith 100 (lets say the difference isD)

2.find the square of D it will give us the last two digits if square

3.find N-D. It will give us the first two digits of the square

example:

Square of 93

100-93=7

7*7=49

93-7=86

So 8649

Collected from bank power app

its very nice trick i liked it

ReplyDeletesir your shortcut tricks were quite good but i would like to know about short cuts for imperfect squares and cubes

ReplyDeleteits really nycccccccccc

ReplyDeletejst i want 2 know how to find cubes in simple process

ReplyDeleteGood techniques sir.keep it up..what is for 3 digits number??

ReplyDeleteCASE I

ReplyDeletesquaring any 2 digit no..

Eg. 83

split 83 to (8|3)^2

8^2=64 and 3^2 =9

8*3*2 =48

64|09

+4|8

____

6889

CASE II

Squaring any 3 digit no..

Split it into 2 parts

Eg.128

(12|8)^2

12^2=144

8^2=64

12*8*2=192

144|64

+19|2

_____

16384

CASE III

Squaring any number ending with 5

Eg. 85

Last 2 digit is 25

Remaining digit is 8*(8+1)

i.e) 8*9 =72

85^2= 7225

Really awesome thank you sir.....

DeleteGreat shortcut... :)

DeleteAmazing

DeleteNice trick. great.....

ReplyDeleteNice trick... Great. It make square calculation so easy.

ReplyDeleteI m giving one more trick may b some people will understand this method...

ReplyDeletefrom number 35 to 75

1. Take value 25 for all squares between this range

2. Square of 48.

3. Take a mid 50 for all.

4. Calculate how less the value is less than 50 then minus it from 25. And the result is 23 and calculate the square of less value i.e. Square of 2 because value is 2 less from fifty the result is 04

5 merge these values result is 2304.

my trick take 53

ReplyDeletefirst take its square 2509 then 5*3=15*2=30 add it like this

2509

30

2809 simpleeeeeeeeeeeeeeeeeeeeeee

yes nice trick... I'm also posting the same trick here...

DeleteFor 2 digit no, adding unitdigit with 10's

For 3 digit no, adding unitdigit with 100's

EG:1004 Split it into two parts : If second part has 2 digits then

10|06

100|0066

1|20

+_______

1012036

Squaring Technique for numbers having same digits...

ReplyDelete>>111 Here there are 3 ones,

so write 123 and in reverse also 321. bt the middle term is common

12321

>>1111 Here 4 ones. 1234321

>>33 here 2 three's are there

3^2=9

write it as _0_9 (single digit gap b4 each digit)

Fill the first gap with next number of 0 i.e)1

Fill the second gap with previous number of 9 i.e) 8

ANS : 1089

>>333

write it as _ _ 0 _ _ 9

Ans : 1100889

Same technique can be applied for 6 and 9

>>666 (6^2 = 36)

write it as _ _ 3 _ _ 6

Ans : 443556

>>999 (9^2 = 81)

write it as _ _ 8 _ _ 1

Ans : 998001

Thanks I got easy technique

ReplyDeletesir how can we do squaring of 4 digits like...1432 nd more than 4 digits like...5432819 etc with shortcuts ?

ReplyDeletehello sir how can we find out the sqaure of 1432 with shortcuts nd more than 4 digits like 73214,5432819 etc ?

ReplyDelete45*45 this another simple way is take last digit multiply 5*5=25....................then take 4 next number of 4 is 5 so multiply both we get 4*5 =20 so 45*45= 2025

ReplyDeleteplease tell the method of squaring 149*149

ReplyDelete(150-1)*(150-1)=22500+1-2(150)=22201

Delete149*149 => FIRST ADD 149 WITH 49 OF SECOND DIGIT 149+49=198 THIS IS OUR FIRST PART ANSWER FOR SECOND PART JUST MULTIPLY 49 OF FIRST ONE WITH 49 OF SECOND ONE =49*49 NOW WE HAVE ALREADY GET FIRST PART NOW SECOND PART JUST ADD BOTH OF THEN AS

ReplyDelete198

2401

22201

hello sir....in 53 square u have taken 3*3 and in 69 square u have taken 1*1....can u tell me y u have taken and the trick?

ReplyDeletehello guys

ReplyDeleteby using this formula ,u can find out square of any number.

Deletesquare of 45=?

a=4,b=5

use it a^2+2ab+b^2 ,put last digit only and remaining will be remainder.

2025

BERBIYA YOUR TECHNIQUE IS SO NICE THANKS FOR GIVING YOUR IDEA.

ReplyDeleteHI BARBIA YOUR TECHNIQUE IS REALLY NICE BUT I HAVE A DOUBT IN THAT CAN YOU PLEASE CLARIFY THAT.IN FINDING CUBE ROOTS I HAVE NO DOUBTS IN FINDING 666 AND 333 AND 999 IS SO BUT THE SAME FORMULA IS NOT APPLICABLE FOR FINDING 444 AND 555 Y I AM CONFUSED PLEASE CALRIFY MY DOUBT SIR

ReplyDelete