*Whatever the deficiency subtract that deficit from the number and write along side the square of that deficit.It is also called as*

__Definition :__**Yaavadunam Sutra**

This sutra is helpful in finding squares and cubes of any two digit-numbers .It can extend up to any number of digits for finding the square and cubes of that particular number. But here I'm going use this sutra with different methods for finding squares for any two-digit and three-digit numbers .

**Method 1 :Using the Yaavadunam Sutra**

1. 98 x 98 =9604

__Steps:__

- The nearest power of 10 to 98 is 100.So we take our base value as 100.(Note: Base values should always be powers of 10)
- We can see clearly that 98 is 2 less than 100.So we call this 2 as deficiency.
- Decrease the given number further by an amount equal to the deciency , meaning ( 98 -2 = 96).Now,this 96 becomes the left side of our answer.
- On the right hand side, put the square of the difiency .i.e; 2 x 2= 04
- Now for the final answer add(append), the results from Step 3 and Step 4.

**Therefore , 98 x 98 =9604**

**Method 2 : Using Duplex Formula**

__Duplex Method Formulas:__

D(X)= X^2

D(XY)=2 XY

D(XYZ)=(2XZ)+Y^2

D(ABCD)=(2AD) +(2BC)

D(ABCDE)=(2AE)+(2BD)+C^2

Following below are few examples :

**3. Squaring any Three-digit Numbers :**

__Exercise :__**To Obtain Squares of any Numbers close to the powers of 10**

To Obtain Cubes of any Numbers close to the powers of 10

plz tell me answer for (534)^2 using duplex method?

ReplyDeleteBy Duplex Method for 534 ^2 ,

Delete= (5x5) = 25

= (2x5x3) = 30

= (2x5x4) +9 = 49

= (2x3x4) = 24

= (4x4)= 16

By adding all the above in sequence, we get

25 + 30 + 49+ 24+ 16

which gives, 285156

Therefore, (534)^2 = 285156

Hope your query is now solved !

Thankx ... :) for the solution..

ReplyDelete