Squaring is multiplying a number by itself.

It is very easy to square two-digit numbers ending in five by using the Vedic Math *sutra* or word formula *“ By one more than the one before.”*

The square of a two-digit number ending in 5 is composed of 2 parts.

- The first or left hand part is obtained by multiplying the ten’s digit “
” or by the next number.*By one more than the one before* - The second part is always 5 x 5 or 25.

Example 15.1: Find **65 ^{2}**

- The first part is the ten’s digit
**6**multiplied by the next number**7**, (so 6 x 7 =*By one more than the one before)***42.** - The second part is always
**25 ( 5 x 5) .** **65**or^{2}= 42|25**4,225**

Even larger numbers can be squared.

Example 15.2: Find **995 ^{2}**

** 995 ^{2} = 99 x 100|25**

** 995 ^{2} = 990,025**

Proof P15: Let t = the ten’s digit; 10t + 5 = two digit number ending in 5(10t + 5)^{2} = (10t)^{2} + 2(10t)(5) + 5^{2}= 100t^{2} + 100t + 25= 100(t^{2} + t) + 25= 100(t)(t + 1)+ 25 |

We can extend the technique to decimals and fractions.

Example 15.3: **3.5 ^{2} = 3 x 4 | .5 x .5 = 12.25**

Example 15.4: **(7 ½) ^{2} = 7 x 8 | ½ x ½ = 56 1/4**

Exercise 15: Find the square of the following numbers

- ) 45
- ) 95
- ) 195
- ) 10,005
- ) 10.5
- ) 7.5
- ) 6 ½
- ) 9 ½
- ) 100.5
- ) 0.025

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!

Pingback: 25 Math Short Cuts Answer Key | The MSC Advantage

Pingback: 25 Math Short Cuts | The MSC Advantage

Pingback: Issue 15 – Basketball League & Squaring Numbers Ending in 5 | The MSC Advantage