Mathematics

Vedic Maths

The Squaring of Numbers Ending in 5

If we wanted to square the number 25, i.e. 25 x 25, we would conventionally take 3 lines of working out. Vedic Mathematics merely looks at the Question, applies one of the 16 Sutras,

and solves it Mentally in One-Line. In this case, the Sutra at work is "By One More Than The Previous Digit". Observing that 25 is a 2 digit number, 5 is the last digit, but we are mainly

interested in "The Previous Digit"which is 2. We say, mentally, ""What is One more than Two?"" It is 3. The word ""By"" in the Sutra really means "to multiply".

The setting out for the first half of the answer is thus:

²

To this we tag on the last digit ""5"" squared:

Thus the answer is 625

Similarly, all other numbers that end in 5, when squared, can be done instantly:
15² = 1 x 2 / 5 x 5 = 2 / 25 = 225
35² = 3 x 4 / 5 x 5 = 12 / 25 = 1,225
45² = 4 x 5 / 5 x 5 = 20 / 25 = 2,025
95² = 9 x 10 / 5 x 5 = 90 / 25 = 9, 025

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Notes

Vedic Maths - Notes

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21. Digital Sums For Multiplication By Eleven

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25. Simple Tricks to multiply

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36. xy as two digit number

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