TO FIND SQUARE OF A 3 DIGIT NUMBER

LET THE 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.

EXAMPLE:

SQ (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.= 2*4*1 +4= 12

  so 2 would be the third last digit  and 1 carryover
STEP 4. Fourth last digit is 2*4*2 + any carryover (which is 1)  = 16+1=17.

 So 7 and carry over 1.
STEP 5. In the beginning of result will be Sq (4) + any carryover from Step 4.

 So 16+1 =17.

So the result will be  177241.


Hope you enjoyed the concept.