What are the multiplicative inverses for K(n)?

Question

$$K(n) =\{x \in \mathbb R: \exists a,b \in \mathbb Q: x = a + b\sqrt n\}$$

With $n \in \mathbb N$, what are the multiplicative inverses $x^{-1}$ for K(n)?

Any advice regarding formatting is greatly appreciated as well since I'm new to all of this.

Answer 1

hint

$$ \frac{1}{a+b\sqrt{n}} = \frac{a-b\sqrt{n}}{a^2 - b^2 n}=*+*\sqrt{n} $$