# MSC 15: Squaring Numbers Ending in 5

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 “By one more than the one before” or by the next number.
• The second part is always 5 x 5 or 25.

Example 15.1:     Find 652

• The first part is the ten’s digit 6 multiplied by the next number 7, (By one more than the one before) so  6 x 7 =  42.
• The second part is always 25 ( 5 x 5) .
• 652= 42|25 or 4,225

Even larger numbers can be squared.

Example 15.2:     Find 9952

9952  =  99 x 100|25

9952  = 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) + 52= 100t2  + 100t + 25= 100(t2 + t) + 25= 100(t)(t + 1)+ 25

We can extend the technique to decimals and fractions.

Example 15.3:     3.52 = 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

1. )   45
2. )   95
3. )   195
4. )   10,005
5. )   10.5
6. )   7.5
7. )   6 ½
8. )   9 ½
9. )   100.5
10. )   0.025

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!

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