Vedic Maths: Square of a Number (Part 3)

In this video of Vedic Math, we will be learning a new method of finding the square of a number. Children from class 9 and above can refer to this method/ sutra to find the square of a number quickly. The method discussed is called the Duplex Method. The Duplex Method is used to find the square of a number is just a single line. In order to carry out this method, one needs to start from LHS and calculate the duplex of a single digit number. Start calculating a duplex of two digit numbers then move two three digit numbers. Similarly, repeat the steps and move towards the rightmost digit. Now, ignore the leftmost digits and start calculating the duplex form the other end one by one. After computing the duplex of all the digits, use a balancing technique to find out the final answer. Refer to the given example. 

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Question: Find the square of 675. 

Answer:

Now, remember the formulae to calculate the duplex of the numbers:

D(a) = a2

D(ab) = 2ab

D(abc) = 2ac + b2

D(abcd) = 2ad + 2bc

D(abcde) = 2ac + 2bd + c2

Applying the formulae to (657)2, we have
 

D(6) / D(65) / D(657) / D(57) / D(76)

62 / 2 x 6 x 5 / 2 x 6 x 7 + 52 / 2 x 5 x 7 / 72 - (Here, Forward Slash ‘/’ indicates balancing technique is used)

 = 36 / 60 / 109 / 70 / 49

 = 4,31,649 

The final answer is 4,31,649.

Stay Tuned to learn more tricks of Vedic Math and do your calculation quickly and easily.