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HOW TO CALCULATE SQUARE OF 3-DIGIT NUMBER
Let the three digit number whose square is to be calculated be XYZ.
(XYZ)2 is calculated like this
STEP 1. Last digit = last digit of (Z)2
STEP 2. Second Last Digit = 2*Y*Z + carryover from STEP 1.
STEP 3. Third Last Digit 2*X*Z+ (Y)2 + carryover from STEP 2.
STEP 4. Fourth last digit is 2*X*Y + carryover from STEP 3.
STEP 5. In the beginning of the result (the first digit) will be (X)2 + 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 147 ?
STEP 1. Last digit = last digit of SQ (7) = 9
STEP 2. Second Last Digit = 2*4*7 + any carryover from STEP 1= 0
STEP 3. Third Last Digit 2*1*7+ Square (4) + any carryover from STEP 2
which is 14+16+ 6 = 36 .
So, 6 would be the third last digit and 3 carryover.
STEP 4. Fourth last digit is 2*1*4 + any carryover (which is 3) = 8+3=11.
So, 1 and carry over 1.
STEP 5. In the beginning of the result will be Sq (1) + any carryover from
Step 4.
So, we get 1+1=2.
Therefore , the square of the number 147 would be 21609
Hope, you enjoyed learning the concept.
Practice the formula with a few more examples. If you practice it often, you
would easily be able to calculate the squares in less than 5-10 seconds.