Amazing technique for calculating easily in your head

http://vedic-maths-ebook.com/vedic
Find out how to calculate 12 squared, 13 squared and 14 squared with this step by step video tutorial.

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[warchife6]

Bet this guy is asian!

[gaussiann]

It is only useful when the leading digit is a 1 (12,13,14,...). The method works like this:

You have some 2-digit number you want to square. Let it be represented by:

10a + b

(So 14 would be a=1, b=4. And 15 would be a=1, b=5. Nice.) Then, the square of 10a + b is:

(10a+b)^2 = 100a^2 + 10(2ab) + b^2. If we get this with his method, then it is correct.

His method says that (10a + b)^2 is:

[ (10a + b) + b] * 10 + b^2

And this is equal to

100a + 10(2b) + b^2.

Thus, his method is only good when a=1

[9308323]

@MaxPlank91 You choose d by the distance (d stands for distance) to the nearest easy number (usually ones that is divisible by 10, doesn't matter. Either end works)

example:

93^2 = (93 + 3)(93 -3) + 3^2 = 8649 OR 93^2 = (93 - 7)(93 + 7) + 7^2 = 8649

You can also:

4267 = (4267 + 267)(4267 - 267 ) + 267^2 =

= 4534 * 4000 + [( 267 + 33)( 267 - 33)]

=18136000 + 71289

=18207289

Like I said, the value of d WON'T MATTER as long as you don't confuse the value to anything else.

[MaxPlank91]

@9308323 How did u choose d?

[9308323]

@gaussiann Not really, this method will work on ANY numbers if understood clearly.

The algebraic expression to explain this trick is:

A^2 = (A + d)(A - d) + d^2

It is indeed fast with if the number you're squaring is less than 20, however, with enough practice, you can solve a much more complicated 2 digit (EVEN 4 DIGITS) in less than a FEW SECONDS MAX (I know, I'm one of those who can do it)

a really impressive but extremely easy number:

999^2=

(999 + 1)(999 - 1) + 1

= 998,001

[MrLynes5]

you guys make it to complicated just use a calculator like the rest of the world.

[hvdenb]

And when you add up X odd numbers starting at 1, you get X^2

For example

1 + 3 + 5 + 7 = 16

there's 4 odd numbers from 1 through 7

16 is 4^2

Practicality decreases exponentially as you add up more odd numbers, but this is something that I discovered myself at age 9 and I remember the thrilll this discovery gave me.

[gwpotgieter]

@HGozzer 32² is actually (2^5)² = 2^10 = 1024 :)

[TheUnPlayable]

Here is my technique to go from a square to another.

exemple: 34² = 1156 so what's 35² ? it's 1156+34+35 :)

That one was easy tho, it works better for bigger numbers :)

[764dak]

@gaussiann His method is similar to mine except mine's better. n^2 = (n+d)(n-d) + d^2.

Eg. Let n =13 and d = 3. 13^2 = 16*10 + 3^2 = 160 + 9 =169

eg2. Let n = 96 and d = 4. 96^2 = 92*100 + 4^2 = 9216.

Another method: (n+d)^2 = n^2 + d(2n +d) rewritten as n^2 = (n-d)^2 + d(2n +d)

These squaring tricks are nothing but manipulation of quadratics. I actually know two more ways of squaring but you're better off using a calculator.