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
8 Comments:
WOW THIS IS REALLY GR8 , I NEVER THOUGHT THIS WAY.
Hi,
I am from South America, I never heard about Vedic Math before... So far, I am amazed with it, but I have one question, where can I get more information about it. Are there any books that you can recommend me about it?
Thanks!
Catalina.
thanks a lot for your reply catalina!.
i suggest you to subscribe to our blog coz we gonna post a lot about vedic maths.
we will also post about the ebook available on the vedic maths.
gaurav
Hi,
How can we apply what should be the base when I want to square 37 or 27 (say)
Regards
Tapan
Hi,
How can we apply what should be the base when I want to square 37 or 27 (say)
Regards
Tapan
the best way in that case is to assume the base is 100/2.
we take 100/2 to keep the propertise of 100 base and also keeping the calculations simple. (50)
if you have any query til now ...plz let me know....
We have a blog that provides some additional Vedic Math tricks that can be helpful for GMAT preparation.
Our latest post shows how you can solve 59 * 51 in 5 seconds!
http://www.Ed4All.org
Oh god! Math is really tricky! There are some people who dislike this subject. On the other hand, if you're able to know the techniques and the magic, you'll start loving math challenges. These tricks can be one of the good lessons to learn. It may be so useful if you're taking GMAT.
Post a Comment