Question

Give an example of two irrational numbers to show that their quotient is an irrational 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

$8\sqrt{15}\&2\sqrt{3}$

On dividing these numbers we get

$\frac{8\sqrt{15}}{2\sqrt{3}}$$=\frac{4\sqrt{3\times 5}}{\sqrt{3}}$

$\Rightarrow \frac{8\sqrt{15}}{2\sqrt{3}}$$=\frac{4\sqrt{3}\times \sqrt{5}}{\sqrt{3}}$

$\Rightarrow \frac{8\sqrt{15}}{2\sqrt{3}}$$=4\sqrt{5}$

where, $4\sqrt{5}$ is again an irrational number

Therefore, the two irrational numbers having their quotient is an irrational number are $8\sqrt{15}$ and $2\sqrt{3}$