Sqaures, Cubes & Fractions

To crack quant (problem solving) part of any entrance test, one needs to be expert in calculations. Faster calculations is one of the key to success in exams. For same one needs to remember Squares, Cubes & Fraction of numbers. Specially from 1 - 20. As it is going to be used very frequently. Believe me it can save time upto 10 mins in a paper which means one can solve 2-3 more question.

I am attaching chart below. Just take few copies and paste it so that you can see everyday.

 Chart for Squares, Cubes & Square roots for numbers 1 - 20.

Ramanujam’s Number:

It is the smallest number which can be written as the sum of two cubes in two different ways. It is a very famous number, so if you dare to proclaim maths as your hobby, you must know it.
Number is 1729=10^3+9^3=1^3+12^3.

Ramanujam Number is 1729.

But allowing negative perfect cubes (the cube of a negative integer) gives the smallest solution as 91 (which is a factor of 1729):

91 = 6^3 + (−5)^3 = 4^3 + 3^3

There is one interesting story on this. Do google search if you have enough time.

_________________________________________________________________________________