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.

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Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

17 thoughts to “How to Find Square of Numbers Ending in 9”

  1. Mr Farooqi
    ii) left the right hand side 9 from the given number; so from 19; 1 will become balance.

    What the hell is left the right hand side 9 ……
    Please use simple English,

  2. 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.

    1. 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.

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