How to Find Square of Numbers Ending in 9
Squaring any number ending in 9
We can easily calculate the square of any number ending in 9 using the method described in this post. Let us understand this method with the help of an example –
Finding the square of 39
Firstly add 1 to the number. The number now ends in zero and is easy to square.
40^2 = (4*4*10*10) = 1600. This is our subtotal.
In the next step, add 40 plus 39 (the number we squared plus the number we want to square)
40 + 39 = 79
Subtract 79 from 1600 to get an answer of 1521. To easily do such subtractions, subtract 80 (1 more than 79) from 1600 to get 1520 and then add 1 to get the answer as 1521.
1600 – 79 = 1521 is the square of 39. Answer.
Another Example of finding the square of bigger number ending in 9.
Finding the square of 159
159^2 =
159 + 1 = 160
160^2 = 25600
160 + 159 = 319
25600 – 319 = 25600 – 340 + 1
25600 – 319 = 25281
Another Example,
449^2
450^2 = 202500 (use the shortcut Squaring number ending in 5 to calculate 45^2 and then put double zeroes in front of the answer)
450+449 = 899
202500 – 899 = 202500 – 1000 + 101 = 201601
To make sure that you have understood the above calculation shortcut, try finding the square of few numbers ending in 9 by yourself – 39, 119, 349.
You may also like:
- Trick to Find Square of Numbers from 51 to 59
- Finding Square of Number Ending in 5
- Shortcut to Find Square of a Number
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I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths
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August 23rd, 2012 - 15:11
thanks….
April 15th, 2012 - 13:53
Farooqi ji excellant
April 10th, 2012 - 00:08
There is also another method for the same:-
Square of 19
i) Subtract 1 from the number ; 19-1 =18
ii) left the right hand side 9 from the given number; so from 19; 1 will become balance.
(iii) in the result of (ii) add 1 i.e. 1+1 =2
(iv) multiply the result of (i) with result from (iii) i.e. 18*2 =36
(v) write 1 on R.H.side of the answer of (iv) i.e. write 1 with 36 it will 361
So (19)2 = 361
similarly for (49)2=
i) 49-1 =48
ii) 4+1 =5
iii) 48*5 = 240
iv) write 1 on Right Hand side of the result of (iii)
So answer = 2401.
April 26th, 2012 - 08:11
thank u.
May 20th, 2012 - 03:20
It is only applicable for the numbers ending with 9!!
June 9th, 2012 - 17:19
19 x 19 = ( 20-1) ( 20 -1) = ( a – b )^2 = a^2 – 2ab + b^2 where a= 20 , b = 1 . 20^2 – 2 x 20 x 1 + 1^2 = 400 – 40 + 1 = 361.
April 6th, 2012 - 13:47
very nice to solve
April 2nd, 2012 - 17:55
thank u very much…
April 2nd, 2012 - 13:45
Sir thank you very much.
April 2nd, 2012 - 13:13
Give something new information.
This old stuff is known to everybody.