Squaring numbers ending in 5

Squaring is multiplying a number by itself.

Squaring numbers ending in five can be simplified using the Vedic Mathematics Sutra “By One More than the One Before”

Let us first take the case of squaring a two-digit number like 65. Here the number before 5 is the ten’s digit, 6. The answer will have two parts: The first is obtained by multiplying 6 by One More than 6 or 7, that is 6 x 7 = 42.

The second part is 5 x 5 or 25. Thus 65^5 = 4225.

Similarly we have 35^2 = 3 x 4| 5 x 5 = 1225 and 85^2 = 8 x 9 | 5^2 = 7225.

For a three-digit number like 195 to be squared, the same procedure can be followed. The number before 5 here is 19, not just 9. And One More than 19 is 20.

We have 195^2 = 19 x 20| 5^2 = 38025

For our example, 66665^2, we have 6666 x 6667|25 or 4444222225  

Even very large numbers like 99, 999,995 can be squared using this method: 99,999,995^2 = 9 999 999 x 10 000 000 = 9,999,999,000,000,025

This method can also be used in decimals and mixed fractions.

Practice exercises:

1. 25^2 =
2. 75^2 =
3. 115^2 =
4. 125^2 =
5. 305^5 =
6. 505^2 =
7. 1005^2 =
8. 3335^2 =
9. 66665^2 =
10. 0.000055^2 =

Answers to last week’s exercises:

1. 791 → divisible by 7
2. 946 → divisible by 7
3. 973 → divisible by 7
4. 1701→ divisible by 7
5. 1847 → not divisible by 7
6. 7154 → divisible by 7
7. 13209 → divisible by 7
8. 17431 → not divisible by 7
9. 42791 → divisible by 7
10. 54999 → divisible by 7