Question

Give an example of two irrational numbers to show that their quotient is a rational number.

Answer 1

Irrational numbers:

Irrational numbers are the number having non-terminating and non- recurring decimals.

Let us assume the two irrational numbers be

$6\sqrt{50}\&3\sqrt{2}$

On dividing these numbers we get

$\frac{6\sqrt{50}}{3\sqrt{2}}$$=\frac{6\sqrt{5\times 5\times 2}}{3\sqrt{2}}$

$\Rightarrow \frac{6\sqrt{50}}{3\sqrt{2}}$$=\frac{2\sqrt{5\times 5\times 2}}{\sqrt{2}}$

$\Rightarrow \frac{6\sqrt{50}}{3\sqrt{2}}$$=\frac{2\times 5\times \sqrt{2}}{\sqrt{2}}$

$\Rightarrow \frac{6\sqrt{50}}{3\sqrt{2}}$$=10$

Where, $10$ is rational number

Therefore, the two irrational numbers having their quotient as a rational number are $6\sqrt{50}\&3\sqrt{2}$