Question

Find the product of following with its conjugate pair.

$\sqrt{3}-\sqrt{2}$.

• A. conjugate pair $=\sqrt{3}-\sqrt{2}$, product $3$
• B. conjugate pair $=\sqrt{3}-\sqrt{2}$, product $1$
• C. conjugate pair $=\sqrt{3}+\sqrt{2}$, product $1$
• D. conjugate pair $=\sqrt{3}-\sqrt{2}$, product $2$

Answer 1

The correct option is C conjugate pair $=\sqrt{3}+\sqrt{2}$, product $1$

The number given is $\sqrt{3}-\sqrt{2}$.

Then, its conjugate is $\sqrt{3}+\sqrt{2}$.
Now, the product is $(\sqrt{3}-\sqrt{2})\times (\sqrt{3}+\sqrt{2})={\sqrt{3}}^2-{\sqrt{2}}^2$ (by applying the identity)
$=3-2=1$.

Therefore, option $C$ is correct.