Some neat vedic math tricks

SQUARING OF NUMBERS NEAR THE BASE.

Observe simple examples:

97 Squared = 97 -­ 3 / 3x3 = 94 / 09
96 Squared = 96 -­ 4 / 4x4 = 92 / 16.

When the number being squared is above the base, of 100 here, we add the Excess and Square the Excess:
104 Squared = 104 + 4 / 4x4 = 108 / 16 = 10, 816
104 x 105 = 104 + 5 / 4x5 = 109 / 20 = 10, 920

What if we enlarged our numbers to 998 Squared?

It is close to 1,000 so we say Base 1,000 and know to have 3 zero's on the right hand side of the ( / ).
998 Squared = 998 -­ 2 / 2x2 = 996 / _ _ 4 = 996 / 004. = 996,004

Understanding this, you can be calculating digits in the millions: 9998 Squared = 9998 -­ 2 / 2x2 = 9996 / _ _ _ 4
(Since we are in Base 10,000 the 4 zeros determine the need for 4 digits after the ( / ). = 9996 / 0004 = 99,960,004.

THE SQUARING OF NUMBERS ENDING IN 5

If we wanted to square the number 25, ie 25 x 25, we would conventionally take 3 lines of working out. Vedic Mathematics merely looks at the Question, applys one of the 16 Sutras, and solves it Mentally in One-Line. In this case, the Sutra at work is "By One More Than The Previous Digit".

Observing that 25 is a 2 digit number, 5 is the last digit, but we are mainly interested in "the Previous Digit" which is 2.
We say, mentally, "What is One more than Two?" It is 3. The word "By" in the Sutra really means "to multiply".
The setting out for the first half of the answer is thus:
25 Squared = 2 "By" 3 / ........ = 2 x 3 / ........ To this we tag on the last digit "5" squared: = 2 x 3 / 5 x 5 = 6 / 25
Thus the answer is 625.

Similarly, all other numbers that end in 5, when squared, can be done instantly:
15 Squared = 1 x 2 / 5 x 5 = 2 / 25 = 225
35 Squared = 3 x 4 / 5 x 5 = 12 / 25 = 1,225
45 Squared = 4 x 5 / 5 x 5 = 20 / 25 = 2,025
95 Squared = 9 x 10 / 5 x 5 = 90 / 25 = 9, 025

Hi friends

We will be continuing with our vedic maths lessons after this post . This is for convenience of those friends who have just started reading the blog and are new here and want to find the GMAT preparation material i previously released on this very blog.
Following are the links to the material I published in earlier posts.

1. Download GMAT material
   
2. More GMAT resources
3. Quant resources
4. Some useful GMAT resources
   

VADIC MATHS - LESSON NUMBER TWO.

after learning how to square a number ending with 5 now we will do something called comman base method.

this method is a technique of multiplying number which comes under same base.
this base could be anything like
-10
-100
-1000 etc.

to multiply two numbers we just need to make them subtracted or added to a comman base.
lets do an example.
MULTIPLY 99 X 92

step 1:-MAKE COMMAN BASE
here the base is 100. (coz while setting the base we should keep in mind that the base should be closest to the numbers to make sure that the minimum calcultaions will be required.

step 2:-SUBTRACT THE NUMBERS FROM THE BASE AND WRITE THEM IN THE ORDER.

100- 99 = 01
100- 92 = 08
(we write the number we get after subtraction in as many digits as many zeros we have in the base, here we have 2 zeros in 100)
AND YOU HAVE TO WRITE THESE IN THE FOLLOWING SEQUENCE

99 01
X !
92 08
----------
91 08 = 9108 is the answer


this 91 we get my subtracting (92-01) or (99-08) cross digits
and 08 we get by multipling the straight line of the digits we get after subtraction from base (01 X 08)
the zero wil remain coz we have two digits in our base.

isnt it simple

now lets try this with two digits which
one is bigger than base another is smaller than base

112 X 92

so step 1:-
112-100 = +12 (no need to add zero coz we have only two zeros in base and we have two digits in 12 as well)
92-100 = -08 (the sign will be on negative coz 92 is lesser than 100)

(in the previous example we ignore negative sign by subtracting both the digits from 100 but in this case its not possible)

so now we have

112 +12
92 -08
-------------
104 -96

now we have to right it like this

10400
- 96
-----------
10304 thats the answer
-----------

you can try this on any number

try it

tables are still important

learn from 1X30 to 30X30

we will keep posting more tricks till then master these ones

gaurav