Question

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

• A. $\sqrt{5},\sqrt{2}$
• B. $\sqrt{8},\sqrt{2}$
• C. $\sqrt{3},\sqrt{2}$
• D. $\sqrt{7},\sqrt{2}$

Answer 1

The correct option is B $\sqrt{8},\sqrt{2}$

Consider option $A$.

The number are $\sqrt{5}$ and $\sqrt{2}$.
Their quotient $\frac{\sqrt{5}}{\sqrt{2}}=\sqrt{\frac{5}{2}}$, which is an irrational number.

Consider option $B$.

The number are $\sqrt{8}$ and $\sqrt{2}$.
Their quotient $\frac{\sqrt{8}}{\sqrt{2}}=\sqrt{\frac{8}{2}}=\sqrt{4}=2$, which is a rational number.

Consider option $C$.

The number are $\sqrt{3}$ and $\sqrt{2}$.
Their quotient $\frac{\sqrt{3}}{\sqrt{2}}=\sqrt{\frac{3}{2}}$, which is an irrational number.

Consider option $D$.

The number are $\sqrt{7}$ and $\sqrt{2}$.
Their quotient $\frac{\sqrt{7}}{\sqrt{2}}=\sqrt{\frac{7}{2}}$, which is an irrational number.

Therefore, option $B$ is correct.