**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.

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,

Thank you sir

great sir

that’s gooooood…..

thanks….

Farooqi ji excellant

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.

thank u.

It is only applicable for the numbers ending with 9!!

For all numbers, “duplex method of squaring” is used.

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.

very nice to solve

thank u very much…

Sir thank you very much.

Give something new information.

This old stuff is known to everybody.