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 (a^{2} and 2ab).

Duplex of a number |

• For a single-digit number, duplex is its square.
**Ex:** Duplex of 8 is: 8^{2} = 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) + 4^{2} = 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.