Question

In number systems there are some formulas please send them and also tell me how we can find that if any number is rational or irrational very clearly

Answer 1

. Basic Formulae

1. (a+b)2=a2+b2+2ab

2. (a−b)2=a2+b2−2ab

3. (a+b)2−(a−b)2=4ab

4. (a+b)2+(a−b)2=2(a2+b2)

5. (a2−b2)=(a+b)(a−b)

6. (a+b+c)2=a2+b2+c2+2(ab+bc+ca)

7. (a3+b3)=(a+b)(a2−ab+b2)

8. (a3−b3)=(a−b)(a2+ab+b2)

9. (a3+b3+c3−3abc)=(a+b+c)(a2+b2+c2−ab−bc−ca)

10. If a+b+c=0, then a3+b3+c3=3abc.

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.
The number 8 is a rational number because it can be written as the fraction 8/1.
Likewise, 3/4 is a rational number because it can be written as a fraction.
Even a big, clunky fraction like 7,324,908/56,003,492 is rational, simply because it can be written as a fraction.
Every whole number is a rational number, because any whole number can be written as a fraction. For example, 4 can be written as 4/1, 65 can be written as 65/1, and 3,867 can be written as 3,867/1.