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# Vedic Math

Square of two-digit numbers

Published: 09th July 2015 06:04 AM  |   Last Updated: 09th July 2015 06:04 AM   |  A+A-

Last week we discussed the squaring of numbers with 5 as the units digit. Now we will look at a method to find the square if the number is near a base. Let us recollect the steps: If a number is less than the base, subtract the decrement to the number to get the first part of the answer and then square the decrement to get the second part of the answer.

If the number is greater than the base then add the increment to the number to get the first part of the answer and square the increment to get the second part of the answer.

Numbers higher than the base

Let us find the square of 106

•  The base is 100 and the increment is 6.
•  Add 6 to 106. 106 + 6 = 112, the first part of the answer.
•  Square the increment. 62 = 36, the second part of the answer.
•  Put the parts together.

Numbers lower than the base

Let us find 932

•  The base is 100. The decrement is 7.
•  Subtract 7 from 93. 93 – 7 = 86, the first part of the answer.
•  Square the decrement. 72 = 49,  the second part of the answer.
•  Combine the parts.

Square of any two-digit number.

This has three simple steps.

1. Square the tens digit.

2. Multiply 2 x first digit x second digit.

3. Square the units digit.

Combine the parts to get the answer.

Example: 342

32 = 9

2 x 3 x 4 = 24

42 = 16

Combine the parts, carrying over where required. The 1 of 16 is carried over to 24, giving 25. The 2 of 25 is carried over to 9, giving 11.

9 24    16

11   5    6

682

1.  62 = 36

2 x 6 x 8 = 96

82 = 64

The 6 of 64 is carried over to 96, giving 102. The 10 of 102 is carried over to 36, giving 46.

36    96           64

36     102          4

46        2            4

Tip of this week: Decide the method depending on the question.