With this trick you can find the square of a number having only ‘9’ such as numbers are 99, 999, 9999 etc.
Short trick:
Let the total number of 9’s be n .Now write 9 up to (n-1) times followed by single digit 8 and then write 0 up to (n-1) times followed by single digit 1. You will be able to understand it better with the help of example.
Therefore,
(999…. )2 = 9 upto [n-1]times|8|0 upto [n-1]times|1
Suppose we need to find the square of 999.
Solution:
Here, number of ’9’ is 3. Therefore n = 3. Now
(999)2 = 99…[3-1 times]|8|00..[3-1 times]|1
= 99…[2 times]|8|00..[2 times]|1
= 99|8|00|1
= 998001
Find the square of 9999.
Solution:
Here, number of ’9’ is 4. Therefore n = 4
(9999)2 = 99…[4-1 times]|8|00..[4-1 times]|1
= 99…[3 times]|8|00..[3 times]|1
= 999|8|000|1
= 99980001
Simirarly you can find squares of numbers like 99999, 999999…..etc.