Shortcut to Find Square of a Number
Today I will discuss a very simple method of finding square of numbers between 26 to 74 mentally. In the subsequent post we will cover higher numbers. So keep watching this space to learn squaring any number within your mind
Square (also called perfect square) is an integer that is the square of an integer; in other words, it is the product of some integer with itself. So, for example, 9 is a square number, since it can be written as 3 × 3.
How to find the square of any number?
To apply this method you should know squares of 1 to 25 by heart. You can refer to this table to learn the same.
| Number | Square | Number' | Square' |
| 1 | 1 | 13 | 169 |
| 2 | 4 | 14 | 196 |
| 3 | 9 | 15 | 225 |
| 4 | 16 | 16 | 256 |
| 5 | 25 | 17 | 289 |
| 6 | 36 | 18 | 324 |
| 7 | 49 | 19 | 361 |
| 8 | 64 | 20 | 400 |
| 9 | 81 | 21 | 441 |
| 10 | 100 | 22 | 484 |
| 11 | 121 | 23 | 529 |
| 12 | 144 | 24 | 576 |
| * | * | 25 | 625 |
For finding square of any number between 26 to 75
Step 1. Find the difference between 50 and the number you want to square.
Scenario 1: If the number to be squared is greater than 50
Step 2. Add that many 100s to 2500 (which is the square of 50)
Step 3. Then add the square of the difference to the result of step 1
Scenario -2: If the number is less than 50
Step 2. Subtract that many 100s to 2500.
Step 3. Then add the square of the difference to the result of step 1
Example
Find out the Square of 67.
Step 1. Difference of 67 and 50 = 67-50 = 17
Step 2. This number is greater than 50. So add 1700 to 2500 = 4200
Step 3. Add square of 17 to step 2.
Answer = 4200+ 289 = 4489
Alternative method of calculating the square of a number:
Since, 67-50 = 17
67^2
We will be getting answer in 2 parts; see below – right hand side gives you tens and units digit. Left hand side gives you the remaining digits.
= 25 + 17 | (17)^2 ( | denotes separation )
= 42 | 289 (17^2 is 289. The 2 shown in subtext will be carried over and added to left hand side)
= 4489
You may also like:
- Trick to Find Square Root
- Trick to Find Square of Numbers from 51 to 59
- Vedic Multiplication of two numbers close to Hundred
Who is behind QuickerMaths?
I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths
I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more
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May 8th, 2013 - 23:28
Check out ..http://kentbrewster.com/square-any-two-digit-number/
good method then this.
March 24th, 2013 - 17:52
DID NT UNDERSTAND
February 16th, 2013 - 17:58
456766664
February 16th, 2013 - 17:58
nice 1
February 16th, 2013 - 17:57
nice method..very helpful
January 8th, 2013 - 18:19
2^32=? Pls work out it in a simple method?
December 19th, 2012 - 15:16
To find the square of any number:
square(25)= sq(2)sq(5)+20*2*5
= 0425+200
= 625
square(115)= sq(11)sq(5)+20*11*5
=12125+1100
=13225
April 2nd, 2012 - 15:02
For sqaure root:-
(for all non perfect sqaures)
Find two perfect squares that your square falls between. For example if I am trying to find the square root of 12, then I know my number is going to fall between the square root of 9 (3^2=9) and the square root of 16 (4^2=16).
Divide your square by one of these two square roots. Therefore, I am going to divide my square, 12, by one of the square roots 3 or 4. I will choose 3. So, 12/3 = 4.
I will average the result from Step 2 with the root I divided by. So, I take my answer from Step 2 (4), and will average this with the root I chose to divide my square by in Step 2 (3). Therefore, (4+3)/2 = 3.5. The square root of 12 is 3.5!
try this with large numbers. for very small numbers like 2, 3 etc it doesn’t work i.e. as you try to find the square root of larger numbers you will get more precise answer……
April 18th, 2012 - 18:22
I know one easiest way to find the square root.
Ex: I want to find out the square of 76
Explanation :
a) 76 is nearer to 80 than 70
b) square of 80 is 6400 we know that ( 8* 8 = 64*100= 6400)
c)know multiply the 80 with twice difference of 80 and 76 (80-76 =4) (4*2 =8)
d) 8*80 = 640
e) subtract 640 from 6400 and add 6 (it is the last digit of 6 sqare) at ones digit. you got the answer
Exception=
1) if the number ends with 4 we need to add 16 or ends with 5 we need to add 25
April 18th, 2012 - 18:27
if we go with the 70 and 76 then simply add(76-70) 6*2*70+4900+36
April 26th, 2013 - 20:19
find square root of 15 using ur formula..
April 2nd, 2012 - 15:01
For sqaure root:-
(for all non perfect sqaures)
Find two perfect squares that your square falls between. For example if I am trying to find the square root of 12, then I know my number is going to fall between the square root of 9 (3^2=9) and the square root of 16 (4^2=16).
Divide your square by one of these two square roots. Therefore, I am going to divide my square, 12, by one of the square roots 3 or 4. I will choose 3. So, 12/3 = 4.
I will average the result from Step 2 with the root I divided by. So, I take my answer from Step 2 (4), and will average this with the root I chose to divide my square by in Step 2 (3). Therefore, (4+3)/2 = 3.5. The square root of 12 is 3.5!
try this with large numbers. for very small numbers like 2, 3 etc it doesn’t work i.e. as you try to find the square root of larger numbers you will get more precise answer……
March 30th, 2012 - 20:39
sir,
how can i find the square root of a number which is more than 4 digit( using short process)
March 2nd, 2012 - 00:28
How to find the square root of a number like 2750.25??
November 27th, 2011 - 07:23
18623787961
November 27th, 2011 - 07:16
just square 5*5 and keep 25 a side and multiply 7*8 =56 then join them i.e 5625 answer
its wery easy to find square of the two digit num ending with 5
for example
hey let me tel abt the suaring of two digit number ending with 5′s
for ex take 25*25
step 1: multiply 5*5=25
step 2:multiply 2*3=6
the answer is 625
first of all wen u see 25*25 nd 35*35 etc wen ever u fing 2 digit numbers ending with 5 you just write 25 atlast and then multiply the first num with the conseqte num as shown above
if it is 45*45
u just write last 25
and multiply 4*5=20
so answer is 2025
June 23rd, 2012 - 16:12
really nice tip..very thankful to u..
February 11th, 2013 - 20:42
but i want to ask you that in the case of 25*25, why we should multiply 2*3?
October 29th, 2011 - 21:09
its good
October 19th, 2011 - 10:04
hi,thank u very much was very much helpfull.
September 17th, 2011 - 13:14
Is there any trick to find square of a 9 series number like 99, 999, 9999 and so on?
June 23rd, 2012 - 22:05
yes
September 4th, 2011 - 21:37
Sir i request u.
i m very confused in square form but i rember 1……..to ….30 sq.and qube form plz help me y any tricks find for any no. of squre….
February 14th, 2012 - 16:32
for two digit square we are having only 9 simple formulas by that we can square all the two digit numbers mail me if u need it
ashok.gujjula@gmail.com
June 23rd, 2012 - 16:16
can u plzzzzz mail me those 9 simple formulae…plzzzz
August 29th, 2011 - 23:47
can anybody tell me how to find square of 25-50 and more than 100 from the same trick
February 15th, 2012 - 19:29
25-50 square trick with example
June 23rd, 2012 - 22:07
for any two numbers ending with 5 we can easyly find the square
if it is 45*45
u just write last 25
and multiply 4*5=20
so answer is 2025
August 29th, 2011 - 18:45
sir pls give the trick for find out the square of greater than hundred
September 28th, 2011 - 20:24
if the no is 105 then
1.take last 2 digit & squre it,write down in rhs,i.e.25
2.get diff bet 100 & 105 i.e. 5
3.add it to original no, 105+5=110,write in lhs
4. answer=11025
March 2nd, 2012 - 00:37
How to find the square of no. 123??
August 14th, 2011 - 13:37
i want to know how to find the square of 136469
August 12th, 2011 - 18:44
hei i know many shortcuts .. i’ll help u catch me at karthikthebest007@gmail.com . iam very very interested and eager in maths . bye…….
August 13th, 2011 - 14:42
kk.
.. i’ll mail u.
August 14th, 2011 - 13:48
If you want to share anything special with all the QuickerMaths.com readers, send it to me at vineetpatawari@gmail.com. If useful, I’ll post it on QuickerMaths.com.
March 14th, 2012 - 14:14
plz help me ,tell me shorcuts of probability ,if u have fb account ,then plz contact me
May 30th, 2012 - 22:57
hey contact me on jay_nfs@yahoo.in for probability shortcuts
August 9th, 2011 - 13:35
how to solve suare root of number greater than 75 ??
August 9th, 2011 - 13:34
how to find square root of number <75 ??
February 14th, 2012 - 16:30
nt only <75 for two digit square we are having only 9 simple formulas by that we can square all the two digit numbers
u can mail me if u want
February 15th, 2012 - 22:29
plz give….
August 8th, 2011 - 20:45
HI !
LEARN THE SQURE ROOT OF 1 TO 25
August 8th, 2011 - 20:43
HI,
CUBE ROOT OF 512000
STEP1 :- CLOSE THE LAST THREE NUMBERS AND THE REMAINND NUMBERS =512
SEE THE IN WHICH NUMBER IS THERE IF IT IS IN BETWEEN THEN LEAST NUMBER CUBE
STEP2 :- AND YOU SEE THE LAST NUMBER 0 IS 0 AND IF IT IS 4 THEN YOU SEE THE CUBE ROOT OF 4 IS 64 YOU SEE ONLY LAST NMBER
November 24th, 2011 - 15:31
plz explain it with example.
February 20th, 2011 - 19:40
There is another easy method….
eg : 37 ^2
Step I (Divided into three parts)
Write as 3^2 | 2 * 3 *7|7^2
Step II
Leave on carry to the next part so that only one digit is left in 10th and unit’s place
Then we get 13 | 7 |9
August 12th, 2011 - 16:43
please explain Step 2 once again clearly sir!!!
August 14th, 2011 - 14:04
Thanks Gokul for your suggestion. BTW the answer is 1369 and not 1379.
Actually this is an application of the formula: (a+b)^2 = a^2 + 2*a*b + b^2; here a = 30 and b = 7.
Arranging the same thing vertically will make it easier for you to understand –
900
420
49
——-
1369
If written in the manner suggested by Gokula (vedic maths way), it becomes simpler.
December 14th, 2010 - 13:43
sir u all r doing a great job
thanx Q so much 4 providing such a marvelous trick of finding a square….thank u so much sir…
November 26th, 2010 - 14:47
ya gud trick it works
November 18th, 2010 - 16:37
What is the best way to start planting a flower garden?
November 16th, 2010 - 11:19
if u wanna multiply 2digit number wid D another 2 digit number i hve 1 simple trick wic i wanna share wid U all
e.g
31 X 41
den 1st a fall multiply 1st digit of one number wid D 1st digit of another number (like 3 X 4)
u will get D first 2 digit of ur ans. i.e 12
12 _ _
den multiply 2nd digit of 1st number wid D 2nd digit of another number (like 1X 1)
den u will get D last digit if ur ans i.e 1
12_ 1
know 1 middle digit is remaining
4 this u hve 2 do RAINBOW multiplication
means u hve 2 find D product of outside digit & den inside digit
after this add the product of inside digit and outside digit [ 3 X 1(outside digit) + 4 X 1(inside digit) ]
here u get D result 7
1271 is D ans
by this method u can easily find out D square also
May 21st, 2011 - 16:16
23*45 pls solve vid dis method
November 16th, 2010 - 10:40
sir u all r doing a great job
thanx Q so much 4 providing such a marvelous trick of finding a square
August 28th, 2010 - 02:57
Hi, afcourse this method is very helpfull for finding the squre and squre root
July 23rd, 2010 - 12:52
103*105=107,added the last term of 105 of value 5
103+5=107
104*104=108
104+4=108
thanx
June 25th, 2010 - 17:27
Thanks Nandeesh for suggesting further simplification. I am glad we have regular contributors like you.
June 24th, 2010 - 10:46
I think that for both the scenarios of whether number is less than 50 or more than 50, same method as scenario 2 will work.
EX: 67
67 – 25 | (17)^2 ( | denotes separation )
= 42 | 289 (17^2 is 289. The 2 shown in subtext will be carried over and added to left hand side)
= 4489
EX: 37
37 – 25 | (13)^2 ( | denotes separation )
= 12 | 169 (13^2 is 169. The 1 shown in subtext will be carried over and added to left hand side)
= 1369
June 22nd, 2010 - 17:44
Hello Dear Nandeesh,
The cases you have mentioned are very specific – I have discussed all of them in my earlier posts
Squaring Number ending in 5 – http://www.quickermaths.com/squaring-number-ending-in-5/
Multiplying 2 numbers, sum of whose units digit is 10 – http://www.quickermaths.com/vedic-multiplication/
I will not say there aren’t simpler methods of finding square than the one mentioned in this post. But this method can be used for large variety of case.
In any case, I appreciate your efforts of describing various methods. I will be happy to post any method suggested by you on QM (if it’s not already published on QM ). I must say your earlier posts were superb.
June 22nd, 2010 - 15:34
With due respect to all, I feel, there are shorter methods for finding squares of numbers without need to remember squares of 1 to 25.
Pl. go through the three tricks below:
1. A quick way to square numbers that end in 5:
75^2 = 5625
75^2 means 75 x 75.
The answer is in two parts: 56 and 25. The last part is always 25.
The first part is the first number, 7, multiplied by the number “one more”, which is 8:
so 7 x 8 = 56
Similarly 852 = 7225 because 8 x 9 = 72.
Before trying to square numbers which do not end in 5, please learn the following trick.
2. Method for multiplying numbers where the first figures are the same and the last figures add up to 10.
add up to 10.
32 x 38 = 1216
Both numbers here start with 3 and the last figures (2 and
So we just multiply 3 by 4 (the next number up) to get 12 for the first part of the answer.
And we multiply the last figures: 2 x 8 = 16 to get the last part of the answer.
And 81 x 89 = 7209
We put 09 since we need two figures as in all the other examples.
3. Method for squaring numbers that do not end in 5.
Ex: 83 x 83 = 83 x (87 – 4) = 83 x 87 – 83 x 4
As explained in trick 2 above, 83 x 87 = 7221.
83 x 4 = 332.
83 x 83 = 7221 – 332 = 6889
June 21st, 2010 - 15:34
@Nikhil: Ofcourse you can use the same method to find the square of numbers greater than 74. But in my next method I will give you the extension of this technique to find squares of number between 76 to 124 and so on.
June 21st, 2010 - 15:30
Hi , this method seems correct, but if I try to find square of say 89 then from your method i need to know (89-50)= 39^2. so in that case we may have to use to this method twice, at first to find 39^2 and then 89^2