Multiplying any number with 11

Ya, ya i know this one is easy but still for those who doesn't know the trick, here it is

Lets take 54 X 11
now simply add 5 and 4 and place the result inbetween the two numbers

so the result would be 594.

Logic behind this would be 54 X (10 + 1) which is 540 + 54. So if you see the tens digit it will be the numbers from the problem.

See its simple.

Now try 32 X 11
it will be 352

Lets step to next level and try 83 X 11
so now add 8 and 3 result is 11 take 1 carry from the tens place and add that to tens digit of the multiplicand
 and place the units digit 1 in between the number.

so the result would be 913.

what if we have 3 digits...... no worry at all
lets take an example 342 X 11
the answer begins with 3 and ends with 2. Now add 3 and 4 and put it after the beginning of the answer. and similarly add 4 and 2 and place it before the last digit of the answer

so the answer would be 3762.

Time to practice more....... Then you will get good hold of this trick.

Enjoy Math 'ing' :)

finding the square, cube and nth power of the number which contains only 9s

• (Number containing 9s)^2 - first write N-1 9s where N is the no of digits in the number, followed by 8 and then followed by N-1 0s, followed by 1

EX: 99^2 = 9801
there are 2 9s so N=2 and N-1 is 1, hence first digit will be 9 followed by 8 and again N-1 zeros and then 1 which is 9801

llly 999^2 = 998001

• (Number containing 9s)^3 - first write N-1 9s where N is the no of digits in the number, followed by 7 and then followed by N-1 0s, followed by 2 and finally N 9s. 

EX: 99^3 = 970299
here you can see only 2 9s so N will be 2 and N-1 wil be 1, hence first digit will be 9 followed by 7 and followed by N-1 0s followed by 2 and finally N 9s

llly 999^3 = 997002999

• (Number containing 9s)^4 - first write N-1 9s where N is the no of digits in the number, followed by 6 and then followed by N-1 0s, followed by 5, again followed by N-1 9s, followed by 6 and N-1 0s and finally 1

EX: 99^4 = 96059601
here you can see only 2 9s so N will be 2 and N-1 wil be 1, hence first digit will be 9 followed by 6 and followed by N-1 0s followed by 5 and then again N-1 9s followed by 6 and N-1 0s finally 1

llly 999^4 = 996005996001

This is how we can easliy find out the nth root of number containing only 9s

To summarize:
for square - remember 8,1 in mind
for cube - remember 7,2
for 4th root - remember  6,5,6

Another way to find the square of the number

Hi Folks,

The first way posted is an oral way of calculating square of a number which doesn't need any piece of paper. Here is the another way to find the square of the number which can be done by paper work(or people who has eidetic memory can try by memorizing).

Here comes the way:

Example: to find 27²

1. First find the square of the units digit and keep the units digit of the result in the answer space and carry the tens digit to the next step i.e 7²=49, so the carry will be 4 and the answer's unit digit will be 9.
2. Now multiply both the digits of a number and make it twice or just multiply all the numbers which are seen in the example i.e 2x7x2  and add the carry  from the previous result to this product. So we will get answer as 32. Now carry 3 to the next step.
3. Lastly square the tens digit and add carry which is carried from the previous step. i.e 2²=4 and adding the carry we will get 7.

So the final result is 729 Tip: memorize (a+b)² = a² + 2ab + b² you will get the way to this.

Come on start thinking and practicing.

Note: The results are mentioned into bold format for your understanding.

calculating the square of the number.

here is one of the simple way to calculate the square number.

Example: 23² = (23+3)(23-3) + 3²

= (26)(20) + 3²

= (26)(10).2 + 3²

= 529

This looks like long procedure but its not!!!

Let me explain:

1. Add the number by the units digit and then multiply with the number subtracted by the same unit digit

2. to multiply added and subtracted numbers is also very simple as i hae shown in the example i.e split the     

    subtracted number in terms of 10's

3. And finally multiply it and add to the square of units digit number.

let me tell you people one more thing 

This shortcut is not a new thing but slight modification of the formula (a²-b²)

 It is modified like this: a²=(a+b)(a-b) + b² .

So try this and keep practicing. Meanwhile will come up with new ideas :)

Hi everyone,

     From now there will be some interesting facts published in this blog which will help u people in many ways....
So keep watching....