# 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:

- 25^2 =
- 75^2 =
- 115^2 =
- 125^2 =
- 305^5 =
- 505^2 =
- 1005^2 =
- 3335^2 =
- 66665^2 =
- 0.000055^2 =

Answers to last week’s exercises:

- 791 → divisible by 7
- 946 → divisible by 7
- 973 → divisible by 7
- 1701→ divisible by 7
- 1847 → not divisible by 7
- 7154 → divisible by 7
- 13209 → divisible by 7
- 17431 → not divisible by 7
- 42791 → divisible by 7
- 54999 → divisible by 7