Mathematics made ease: How to find Square by simple method?

How to find Square?

There are three methods by which you can find Square:

1. Multiplication method: This method is simple for the smaller numbers. Simply we multiply the number by itself.

for instant. 5² = 5 x 5 = 25,

6² = 6 x 6 = 36

25² = 25 x 25 = 625

2. Column method: In this method, the algebraic identity (a + b)² = a² +2ab +b² is used to find the square of a given number. Let us take an example of square of 49. The we take 4 as a and 9 as b

Step1. Make column I, II, III, having headings a², 2 x a x b, and b², respectively. As shown in the table given below. Either the values of a², 2ab, and b² in the respective columns.

Step2. In the III column, underline unit digit of b² and carry forward the tens digit, if any, to column II and add it to the value of 2 x a x b. In execution of this step, 1 is underlined in column III and 8 is carried to column II and added to 72.

Step3:- In column II, underline the unit digits and carry forward the tens digits, if any, to the column I and add it to the value of a². In execution of this step, 0 is underlined in column II and 8 is carried forward to column I and added to 16.

Step 4: Underline the digits of the number obtained in column I. Write down all the underline digits in order starting from column I. The number obtained is the square of the given number.

a = 4 and b = 9

Column I	Column II	Column III
a² 42 = 16 +8 24	2 x a x b = 2 x 4 x 9 = 72 + 8 ______________ 80	b² 9² ________ 81

Hence, (49)² = 2401

Diagonal Method:- This method is more useful when the numbers are bigger. We shall follow the following steps:-

Step 1:- If the given number contains two digits e.g., 57 then we shall draw a square and divide them into 4 small squares. If the given number contains three digits, e.g., 143 then divide the square into 9 small squares. Write the digits of the number (2 digit or 3 digit number as the case may be), vertically and horizontally, as shown in the figures alongside.

Step 2:- Now, multiply each digit on the left of the square with digit on the top of the column, if the product so obtained is a single digit, write it below the diagonal. If it is a two digit number, write the tens digit above the diagonal and the units digit below the diagonal.

Step 3:- Starting with lowest diagonal ( i.e., right hand bottom), add the digits below each diagonal. Underline the unit’s digit, if any, to the diagonal above. Write all the underline digits starting from the topmost diagonal. The number obtained is the square of the given number