# Squaring numbers ending in 5

The Sutra **“By one more than the one before”** is used to **square numbers ending in 5**.

Example 1: What is **35 ^{2}**?

The number **before** **5** is **3** so we will multiply it** by one more than** **3** or **4 ** to get the first part of the answer. **3 x 4** is **12**. And the last part of the answer is always **5 x 5** **or 25. **

**35 ^{2 }= 3 x 4 | 5 x 5 = 12|25 = 1225**

See proof of this in p. 53 of **25 Math Short Cuts **byVirgilio Prudente**.**

This technique can be used with larger numbers.

Example 2: What is the square of **1005?**

The number before **5** here is **100 **so one more than this is **101.**

**1005 x 1005 = 100 x 101 | 5 x 5 = 10100| 25 = 1,010,025**

Example 3: (3335)^{2}=

= 333 x 334 |25 = 111222 | 25 = **11,122,225**

And also with decimals.

Example 4: What is (3.5)^{2}?

This is like Example 3 but 3.5 is exactly a tenth of 35. Whereas before we have 5 + 5 = 10, now we have 0.5 + 0.5 = 1, also a unity

(3.5)^{2} = 3 x 4| 0.5 x 0.5 = 12| 0.25 = 12.25

And fractions.

Example 5: 4 1/2 x 4 1/ 2 =?

Here we have 1/ 2 + 1/ 2 = 1

**4 1/2 x 4 1/ 2** = 4 x 5 | 1/ 2 x 1/ 2 = 20 | 1/ 4 = **20 1/ 4**

Even in area computations:

Example 6: What is floor area of a square room which is 10’ 6” on a side?

Since 6” = 1/ 2 foot, the sutra can also be used here.

10’ 6” x 10’ 6” = 10 x 11 | 6 x 6 = **110 square feet and 36 square inches **

(Taken from pp 3-5 of 30 Master Strategies in Computing, Vol I e-book)