Question

Give an example of two irrational numbers, whose quotient is an irrational number.

• A. $\sqrt{15},\sqrt{5}$
• B. $\sqrt{45},\sqrt{5}$
• C. $\sqrt{20},\sqrt{5}$
• D. $\sqrt{80},\sqrt{5}$

Answer 1

Answer: (A)

$\sqrt{15},\sqrt{5}$

Consider option $A$.

The number are $\sqrt{15}$ and $\sqrt{5}$.
Their quotient $\frac{\sqrt{15}}{\sqrt{5}}=\sqrt{3}$, which is an irrational number.

Consider option $B$.

The number are $\sqrt{45}$ and $\sqrt{5}$.
Their quotient $\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{9}=3$, which is a rational number.

Consider option $C$.

The number are $\sqrt{20}$ and $\sqrt{5}$.
Their quotient $\frac{\sqrt{20}}{\sqrt{5}}=\sqrt{4}=2$, which is a rational number.

Consider option $D$.

The number are $\sqrt{80}$ and $\sqrt{5}$.
Their quotient $\frac{\sqrt{80}}{\sqrt{5}}=\sqrt{16}=4$, which is a rational number.

Therefore, option $A$ is correct.