Finding the Square of a Number
There are several methods to find the square of a number in Mathematics. The method we shall discuss in this topic gives a general procedure of finding square of any number and is based on a process known as Duplex Combination Process.
The term "Duplex" is used in two different senses. The first one is by squaring and the second one is by cross-multiplication. In the present context, it is used in both the senses (a2 and 2ab).
|Duplex of a number
|• For a single-digit number, duplex is its square.
Ex: Duplex of 8 is: 82 = 64.
|• For a two-digit number, duplex is twice the product of the two digits.
Ex: Duplex of 36 is: 2(3 × 6) = 2 × 18 = 36.
|• For a three-digit number, duplex is twice the product of the outer two digits plus the square of the middle digit.
Ex: Duplex of 745 is: 2(7 × 5) + 42 = 70 + 16 = 86.
|• For a four-digit number, duplex is the sum of two products: first, twice the product of the extreme digits, and second, twice the product of the middle two digits.
Ex: Duplex of 4723 is: 2(4 × 3) + 2(7 × 2) = 24 + 28 = 52.
|In the similar manner, we can write duplex for n-digit number.
The process of finding the square of a no. is best illustrated with the help of .
Squaring of numbers ending in 5:
Step 1: Square 5 and put down 25 as the right hand part of the answer.
Step 2: After dropping 5, multiply the number left by a number 1 more than itself. This gives left hand part of the answer.