Faster way to square any number beginning with 5

To square a 2-digit number beginning with 5 at a faster way, just follow:

Step-1:  Add the digit at the unit place to 25 and write the sum; this is the first part of the answer.

Step-2:  Square the unit place digit and write it; this is the last (2-digits) part of the answer. (If it is a single digit answer, place an extra '0' before it to make it a 2-digit number).

Example: If the number to be squared is 58

1.            add 8 to 25, we get 33 (the first part of the answer)

2.            square of 8 is 64 (the last part of the answer)

So, 58² is 3364.

Another example: 53² =?

 

1.    add 3 to 25, we get 28 

2.    square of 3 is 9, write 09 (make sure to place a 2-digit number)

Hence the answer is 2809.

To square a 3-digit number beginning with 5:

Step-1:     Add the last 2 digit to 250 and write the sum; this is the first part of the answer.

Step-2:     Square the last 2 digit and write it; make sure it is takes 3 places by putting extra '0' or carrying forward any extra digit.

For example: 512² =?

 

a)    Add 12 to 250 to get 262. 

b)    Square of 12 is 144.

So, the final answer is 262,144.

Again, 580² =?

a)    Add 80 to 250 to get 330. 

b)    Square of 80 is 6400.

Since 6400 is a 4-digit number place 400 as the last part and carry forward 6 to 330 to get 336.

So, the final answer is 336,400.