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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