Question

Which of the following is the conjugate surd of $-3-\sqrt{8}$?

• A. $-\sqrt{3}-\sqrt{8}$
• B. $\sqrt{3}-\sqrt{8}$
• C. $-3+\sqrt{8}$
• D. $3+2\sqrt{8}$

Answer 1

The correct option is C $-3+\sqrt{8}$

The conjugate pair of the given surd is $-3+\sqrt{8}$.
We can obtain this by interchanging the sign of the surd part, which is $\sqrt{8}$ in this case.

Now, if we multiply both the surd and its conjugate, we get
$(-3-\sqrt{8})(-3+\sqrt{8})=(-3{)}^2-(\sqrt{8}{)}^2=9-8=1$.