Squares of three-digit numbers
Today we look at a method to find the square of a three-digit number. To do this easily we must know the squares of the nine one-digit numbers. The steps involved are:
Square all the digits and write them as two-digit numbers.
Multiply 2, the units digit and the tens digit.
Multiply 2 , the hundreds digit and the units and tens digits taken together as a two-digit number.
Finally placing them in the proper position as shown in the examples and adding them we get the final answer.
Let us look at an example: 2132
First put down the squares of the given 04 01 09
digits as two-digit numbers
Multiply 2 x units digit x tens digit 0 4 0 1 0 9
2 x 3 x 1 = 0 6 0 6
Put the answer in the tens and hundreds
places
Multiply 2 x hundreds digit x units and tens 0 4 0 1 0 9
digits taken together as a single number 0 6
2 x 2 x 13 = 52 5 2
Put the answer in the 100s and 1000s places
Add the numbers as they are placed in the 0 4 0 1 0 9
columns to get the answer 0 6
5 2
0 4 5 3 6 9
Answer: 2132 = 45369
Example: 5282
Squares of the given digits: 2 5 0 4 6 4
2 x units digit x tens digit: 2 x 8 x 2 = 32 3 2
2 x hundreds digit x units and tens digits: 2 8 0
2 x 5 x 28 = 280
2 7 8 7 8 4
Answer: 278784
The important thing is that we need to place the digits correctly and then add along the columns.
We can use this method for for any 3 digit number. May be for bigger numbers the calculation may be bigger but it is surely easier than finding the square in the usual method.
Let us try one more example.
6422 3 6 1 6 0 4
1 6
5 0 4
4 1 2 1 6 4
Answer: 412164
Try these: 2532 5152 3512