Calculate squares of 3 digit numbers

Let the three digit number whose square is to be calculated be XYZ. Sq(XYZ) is calculated like this

STEP 1.         Last digit = last digit of SQ (Z)
STEP 2.        Second Last Digit = 2*Y*Z +  carryover from STEP 1.
STEP 3.        Third Last Digit 2*X*Z+ Sq(Y) +  carryover from STEP 2.
STEP 4.        Fourth last digit is 2*X*Y +  carryover from STEP 3.
STEP 5.         In the beginning of result will be Sq(X) + any carryover from Step 4.

For those who got confused with the above formula, we have some examples shown below:
Examples:
Q. 1) What is the Square of 421
STEP 1.          Last digit = last digit of SQ (1) =1
STEP 2.          Second Last Digit = 2*2*1 + any carryover from STEP 1= 4
STEP 3.          Third Last Digit 2*4*1+ Square (2) + any carryover from STEP 2=8+4=12
As, a result 2 would be the third last digit and 1 is the carryover.
STEP 4.          Fourth last digit is 2*4*2 + any carryover (which is 1) = 16+1=17.
So, 7 is the digit and carry over 1.
STEP 5.         In the beginning  result will be Sq (4) + any carryover from Step 4.
So 16+1 =17.
So the final result will be  177241.

Q. 2) What is the square of 511?
STEP 1.        Last digit = last digit of SQ (1) =1
STEP 2.       Second Last Digit = 2*1*1 + any carryover from STEP 1= 2
STEP 3.       Third Last Digit 2*5*1+ Square (1) + any carryover from STEP 2 which is 10+1=11.
So, 1 would be the third last digit  and 1 carryover.
STEP 4.        Fourth last digit is 2*5*1 + any carryover (which is 1) = 10+1=11.
So, 1 and carry over 1.
STEP 5.        In the beginning of result will be Sq (5) + any carryover from Step 4.
So, we get   25+1=26.
Therefore, the square of the number 511 would be 261121.

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