Vedic Math - Squaring of numbers near '50'

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In this article, we pick another special case of squaring i.e. squaring numbers which are near 50. It can have two cases, which are:

• Case 1: Numbers greater than 50.
• Case 2: Numbers lesser than 50

In both the cases, we need to take 50 as the base value. First let us take 'Case 1' i.e. 'Numbers greater than 50'.

Case 1 -
Take an example: Say, 54²=2916 
Consider this answer in two parts: 29 (first part) and 16(second part). Now let us study, how Vedic Math can help us to achieve this answers or both of these parts.

As we are taking '50' as base, so the number presentation will be like 50 + 4. So the first part is 50, and second part is 4.

For the first part of the answer:

1. Pick the first part i.e. 50.
2. Pick the first digit i.e. 5
3. Square this digit i.e. 5² > 25
4. Add 4(second part) to it
5. And we get our first part of the answer i.e. 29 (25 + 4).

For the second part of answer, following are the steps:

1. Pick second part i.e. 4
2. Square this digit i.e. 4² > 16
3. And we get our second part of the answer i.e. 16

So the answer is 2916

Let us understand it with another example to make it more clear. Say, 61²=3721
As we are taking '50' as base, so the number presentation will be like 50 + 11. So the first part is 50, and second part is 11.

For the first part of the answer:

1. Pick the first part i.e. 50.
2. Pick the first digit i.e. 5
3. Square this digit i.e. 5² > 25
4. Add 11(second part) to it
5. And we get our first part i.e. 36 (25 + 11).

For the second part of answer, following are the steps:

1. Pick second part i.e. 11
2. Square this digit i.e. 11² > 121
3. Now the result is of three digit. So the first digit (1) will be added to the first part i.e. 1 + 36 = 37
4. So first part becomes 37 now
5. And second part of answer will be 21 

So the answer is 3721. Refer to image below for visual representation.