Trick to find cubes of numbers from 11 to 99.

Trick to find cubes of numbers from 11 to 99.

If a 2-digit number is written in form ‘ab’ then a is tens place digit and b is unit place digit.

To find its cube find:  

1)      a x a x a put 3 zeros(000) after it.

2)      3 x a x a x b; put 2 zeros (00) after it.

3)      3 x a x b x b; put 1 zero after it.

4)      b x b x b

5)      Add all of the above to get the required cube of the given 2-digit number.

6)      Trick can be used to find cubes of 11 to 99. Of course 10’s cube is 1000.

Ex. To find cube of 13:

1)      1 x 1 x 1 = 1 =>                                                   1000

2)      3 x 1 x 1 x 3 = 9 =>                                               900

3)      3 x 1 x 3 x 3 = 3 x 3 x 3 = 9 x 3 = 27 =>                  270

4)      3 x 3 x 3 =                                                               27

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5)                                                                        2197

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How to learn tables 2 to 30 smartly?

Make tables  your friend.
How to learn tables smartly.
1) Learn how to add 2 same natural numbers from 1 to 9 quickly. Practise 1 +1, 2+2, ....9+9 many times.
2) 5s are of any table is half of 10s are.
2a) for getting 5s are of even numbers ex. 28;
For dividing 280 by 2. Remember 280=200 + 80. So half of 200 is 100 and that of 80 is 40. Therefore half of 280 is 140.
2b) for getting 5s are of odd numbers ex. 27.
For dividing 270 by 2. Remember 270=200 + 60+10. So half of 200 is 100 and that of 60 is 30 and that of 10 of 5. Therefore half of 270 is 135.
3) 9s are of any table is one time less than once 10s are. Ex. To get 29 9s are: For subtracting 29 from 290 first subtract 20 from 290 so it is 270. Now subtract 9 from 270; answer is 261.
4) Learn by heart only 2s are, 3s are and 7s are of every table.
5) 4s are are double or twice of 2s are.
6) 6s are are double or twice of 3s are.
7) 8s are are double or twice of 4s are.
8) ex. For 14 4s are double 28 (14 2s are). 28 is 20 + 8. 20 + 20 = 40. 8 + 8 is 16. And 40 + 16 is 56 or (40  + 10) + 6 = 50 + 6 = 56.
All the best!