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:

Take an example: Say,

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

Let us understand it with another example to make it more clear. Say,

As we are taking '50' as base, so the number presentation will be like

Now, let us study '

Take an example: Say,

As we are taking '50' as base, so the number presentation will be like

In the second case, we explore the sub-sutra

43

49

56

52

62

Try it. I hope by now you would have understood the method. Even then if you have any difficulty, post your doubts here. Enjoy!!

Please do share your views that would be having great value for us and will encourage us.

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

**Case 1 -**Take an example: Say,

**54**^{2}**=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:**- Pick the first part i.e. 50.
- Pick the first digit i.e. 5
- Square this digit i.e. 5
^{2}> 25 - Add 4(second part) to it
- And we get our first part of the answer i.e. 29 (25 + 4).

**For the second part of answer, following are the steps:**- Pick second part i.e. 4
- Square this digit i.e. 4
^{2}> 16 - And we get our second part of the answer i.e. 16

Let us understand it with another example to make it more clear. Say,

**61**^{2}=3721As 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:**- Pick the first part i.e. 50.
- Pick the first digit i.e. 5
- Square this digit i.e. 5
^{2}> 25 - Add 11(second part) to it
- And we get our first part i.e. 36 (25 + 11).

**For the second part of answer, following are the steps:**- Pick second part i.e. 11
- Square this digit i.e. 11
^{2}> 121 - Now the result is of three digit. So the first digit (1) will be added to the first part i.e. 1 + 36 = 37
- So first part becomes 37 now
- And second part of answer will be 21

Now, let us study '

**Case 2**' i.e. Numbers lesser than 50.**Case 2 -**Take an example: Say,

**48**^{2}**=2304**As we are taking '50' as base, so the number presentation will be like

**50 - 2**. So the first part is 50, and second part is (-2).*For numbers below 50, we take the deficiency from 50 (2 in this case), to get the number (48 in this case); and use the square of the deficiency (2*^{2}*= 4 in this case) for calculation.**:***For the first part of the answer**- Pick the first part i.e. 50.
- Pick the first digit i.e. 5
- Square this digit i.e. 5
^{2}> 25 - Add (-2) (i.e. second part) to'25'
- And we get our first part i.e. 23 (25 + (-2)).

**For the second part of answer, following are the steps:**- Pick second part i.e. (-2)
- Square this digit i.e. (-2)
^{2}= 4 - And second part of answer will be 04

In the second case, we explore the sub-sutra

**"Whatever the deficiency lessen by that amount and set up the square of the deficiency"****The Algebra behind this method is:**-
*(50 + a)*(if number is above 50)^{2 }= 100 (25 + a) + a^{2} -
*(50 - a)*(if number is below 50)^{2}= 100 (25 - a) + a^{2}

**Here are few exercises for your practice:**43

^{2}= ?49

^{2}= ?56

^{2}= ?52

^{2}= ?62

^{2}= ?Try it. I hope by now you would have understood the method. Even then if you have any difficulty, post your doubts here. Enjoy!!

Please do share your views that would be having great value for us and will encourage us.