SQUARING ANY TWO DIGIT NUMBER ENDING IN ONE OR NINE

Squaring any two digit number ending in 1 or 9 is very interesting and easy method. Two digit numbers ending in 1 are from 11 to 91.Two digit numbers ending in 9 are from 19 to 99.

   The trick is to multiply together the two whole numbers on either side of the number you are squaring, and then add one.
Let’s see how it works.
Problem:-
 31x31 (square of 31)
Step 1:-find the two whole numbers on either of 31 that are 30 and 32
Step 2:-multiply the two whole numbers.30x32=960.
Step 3:- add one to 960 The answer is 961.

Square of 31 is 961.
One more example:
61x61
The two whole numbers on either side of 61 are 60 and 62.
Product of 60 and 62 is 3720.
Adding 1 to 3720 we get 3721.
The answer is 3721.

SQUARE OF ANY TWO DIGIT NUMBER ENDING IN 9..
The method is same as above.
Consider an example of any two digit number ending in 9.

Suppose the number is 19.
Step 1:- find the two whole numbers on either side of 19, that are 18 and 20.
Step 2:- multiply the two whole numbers.
 18x20=360.
Step 3:- adding 1 to 360 ,we get 361.
Square of 19 is 361.

This trick makes the calculation easier by changing one of the numbers into a multiple of 10..