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
- ) 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 )!