15963 squared= ?another nine digit number without zeros and nothing repeated ]]>

50 is nearest multiple of ten to 46

{(46+4)*(46-4) }* {4^2}

which breaks to an easy (50*42) + 16 = 2116

It takes 3 to 5 sec if u practice it well

This method was explained in his book ]]>

In order to remember complex numbers like 19475 he has devised a system which compacts the number into a simple word which he can then string together as a phrase.

In math we have seen this method used to take large numbers and break them down into something more legible.

For example a binary string ( a string of 1’s and 0’s) can be extremely hard to remember or write down. But what if the base is converted into something that is easier to use such as Hexadecimal.

Using Hex let’s practice taking this impossibly long string and making it easy

1110111100010111001

Group them by 4 digits

0111 0111 1000 1011 1001

Now directly convert them to their hex equivalent (0 – F)

7 7 8 B 9

See how the hex string 778B9 is easier to remember.

Now imagine that a word is used to remember the complex string.

This is how he is storing the complex numbers.

I know that it can be done. One also knows that some can do it fast.

MY PROBLEM IS : ” How to hold numbers in ones head, in the first place ?? ” Calculations of the bits is easy.

Any hints about how ordinary persons should learn these processes ?

]]>We’ll try squaring 734. Using the method in my previous post, I start with 490916 (squaring each digit individually). Now:

7 * 34 = 238

238 * 200 = 47600

Note that we’ve multiplied by 200 rather than 20 – because we’re one column to the left. Finally:

3 * 4 = 12

12 * 20 = 240

So the square of 734 equals:

490916 +

47600

240

=538756

And now a four-figit number randomly picked out 8126. Again, square the digits individually to get 64010436. Then:

8 * 126 * 2000 = 2016000

1 * 26 * 200 = 5200

2 * 6 * 20 = 240

So 8126^2 equals:

64010436 +

2016000

5200

240

=66031876

I actually do all of this in reverse when I am doing it in my head, squaring the digits individually last. I remember the smaller numbers first and build on them.

Hope this is helpful to anyone who needs to square numbers!

]]>I can square huge numbers in my head; like in the trillions: (4*10^13)^2 = 1.6*10^27. They just have be one or two digits xD

The largest (actual) squaring problem I’ve done is four digits, but then I don’t memorize any digits with a code, and it does take a while.

]]>I find the above method much too complicated to execute in my head, but perhaps I am so stuck in my own method that any other means of squaring numbers is confusing. I have a method of squaring numbers which allows me to square 4-digit numbers in my head. Granted it takes some time (about a minute), but it’s possible. I haven’t found it mentioned anywhere on the Internet, so I thought I would share it here.

Let’s start with an easy number: 12. We all know the answer is 144, but to demonstrate I start by squaring the individual digits.

1 * 1 = 01

2 * 2 = 04

Both answers should be given two spaces, so I end up with 0104. Obviously, we drop the first zero.

Now I multiply the 1 by the 2, and continue to multiply by the magic number 20. I don’t know why 20, but it works, and it is universal. So I have:

1 * 2 * 20 = 40.

Now I add the 40 to the 104 to get 144.

Let’s try something a little less familiar: 83.

Sqaure the individual numbers to get 6409.

8 * 3 = 24.

24 * 20 = 480.

6409 + 480 = 6889 -> Our final answer.

Three- and four-digit numbers requires a couple of extensions of the above rules, but no more difficult. Any thoughts?

]]>