1. So far we have seen History of Vedic Maths Multiplication Squares Division Cube Root Square Root Astronomical multiplication Magical Squares

2.  New Square Root  Cube  Pythogoras Triads  Friendly Numbers  Palindromes  Exciting Arrangement

3. 4 6 2 2 2 5 *2 2 5 0 6 10 1 2 0 4 *2 3 2 0 Let us take numbers 625 and 1024 and find square root Step1: Nearest square root of 6 = 2 Step 2: 6 - 2 2 = 2 Step 3 : Obtain 4 as shown in figure Step 4 : 22/4 = 5 & R= 2 Step 5 : 25/5 => R=0 Try yourself for 1024

4. General formula: (10+x) 3 = (10+3x) / 3x 2 / x 3 Example: 12 3 = (10+2) = 16/ 1 2/8 => 1728 998 3 = (1000-2) 3 = 994 / 012 / 008 => 994011992

5. How many Pythogoras Triads like 3,4,5 you know? Now I will give you a general formula to find triads. General formula: (axa - bxb)(axa - bxb) + 2abx2ab = (axa + bxb)(axa + bxb) (2x2-1x1)(2x2-1x1)+(2x2x1)(2x2x1)=(2x2+1x1)(2x2+1x1)i.e.; 3x3+4x4=5x5 (3x3-2x2)(3x3-2x2)+(2x3x2)(2x3x2)=(3x3+2x2)(3x3+2x2) i.e.; 5x5+12x12=13x13 Thus by putting any value to a and b in the above formula you can get the triads.

6. It is said that when Pythagoras was asked to describe the characteristics of a friend, he replied, 'he is the other I, like 220 and 284. Proper divisors of 220 are 1,2,4,5,10,11, 20,22,44,55 and 110. These add up to 284. Similarly the proper divisors of 284, which are 1,2,4,71, and 142 add up to 220. Thus each is the sum of the proper divisors of the other. Note : Other friendly numbers known are 17296 & 18416 9,363,584 & 9,437,056 1184 & 1210

7. How to obtain a palindrome in number by doing arithmetic operation? Here is an example of getting palindrome 3821 5104 +1283 +4015 5104 9119 which is a palindrome. Note : 3821 when reversed 1283 & 5104 when reversed 4015.

8. 6 2 - 5 2 = 11 56 2 - 55 2 = 111 556 2 - 555 2 = 1111 5556 2 - 5556 2 = 11111 9 2 - 2 2 = 77 59 2 - 52 2 = 777 559 2 - 552 2 = 7777 5559 2 - 5552 2 = 77777

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