Question

What is the multiplicative inverse of $3-\sqrt{8}$ ?

• A. $\frac{1}{3+\sqrt{8}}$
• B. $3-\sqrt{8}$
• C. $8+\sqrt{3}$
• D. $3+\sqrt{8}$

Answer 1

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

Let $x$ be the multiplicative inverse

$\Rightarrow 3-\sqrt{8}\times x=1$

$\Rightarrow x=\frac{1}{3-\sqrt{8}}$

Rationalising the number

$\Rightarrow x=\frac{1}{3-\sqrt{8}}\times \frac{3+\sqrt{8}}{3+\sqrt{8}}$

$\Rightarrow x=\frac{3+\sqrt{8}}{(3{)}^2-(\sqrt{8}{)}^2}=\frac{3+\sqrt{8}}{9-8}=\frac{3+\sqrt{8}}{1}$

$\Rightarrow x=3+\sqrt{8}$

So option $D$ is correct.