Question

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

• A. $4\sqrt{3},2\sqrt{3}$
• B. $\sqrt{3},\sqrt{3}$
• C. $2\sqrt{3},2\sqrt{3}$
• D. $4\sqrt{3},4\sqrt{3}$

Answer 1

The correct option is A $4\sqrt{3},2\sqrt{3}$

Let be the Number are $4\sqrt{3}$ and $2\sqrt{3}$.
Difference of Number $4\sqrt{3}-2\sqrt{3}=2\sqrt{3}$, which is a irrational number.

The numbers in options $B$, $C$ and $D$, on taking the difference gives value $=0$, which is a rational number.

Hence, option $A$ is correct.

Consider option $A$.

The number are $4\sqrt{3}$ and $2\sqrt{3}$.
Their difference $4\sqrt{3}-2\sqrt{3}=2\sqrt{3}$, which is an irrational number.

Consider option $B$.

The number are $\sqrt{3}$ and $\sqrt{3}$.
Their difference $\sqrt{3}-\sqrt{3}=0$, which is a rational number.

Consider option $C$.

The number are $2\sqrt{3}$ and $2\sqrt{3}$.
Their difference $2\sqrt{3}-2\sqrt{3}=0$, which is an rational number.

Consider option $D$.

The number are $4\sqrt{3}$ and $4\sqrt{3}$.
Their difference $4\sqrt{3}-4\sqrt{3}=0$, which is an rational number.

Therefore, option $A$ is correct.