Question

If we add subtract multiply or divide two irrational the result may be rational or irrational. Give two examples for each

Answer 1

Answer:

1 - Irrational +  Irrational = Irrational

- $\sqrt{2}$ + $\sqrt{2}$ = 2$\sqrt{2}$

2 - Irrational  -  Irrational = Irrational or Rational

- $\sqrt{3}$ -$\sqrt{2}$  =  $\sqrt{3}$ -$\sqrt{2}$ ---> Irrational

- $\sqrt{3}$ - $\sqrt{3}$  = 0 ----> Rational

3 - Irrational  *  Irrational = Rational or Irrational

- $\sqrt{2}$ * $\sqrt{2}$ = 2    ----------> Rational

- $\sqrt{2}$ * $\sqrt{3}$ = $\sqrt{6}$  ----------> Irrational

4 - Irrational / Irrational = Rational or irrational

- $\sqrt{2}$ / $\sqrt{2}$ = 1 -------> rational

- $\sqrt{2}$ / $\sqrt{3}$ = $\sqrt{2}$ / $\sqrt{3}$ -----------> Irrational