Question

Simplify (1+√3)(1/3+√3) leaving your answer in the form of p+q√3​

Answer 1

Hello, I assume that you mean.

$\dfrac{1+\sqrt{3}}{3+\sqrt{3}}$

We need to multiply by the ^conjugate^ to get rid of the root at the denominator.

Let's do it!

$\begin{aligned}\\\dfrac{1+\sqrt{3}}{3+\sqrt{3}}&=\dfrac{(1+\sqrt{3})(3-\sqrt{3})}{(3+\sqrt{3})(3-\sqrt{3})}\\\\&=\dfrac{3-\sqrt{3}+3\sqrt{3}-3}{3^2-\sqrt{3}^2}\\\\&=\dfrac{2\sqrt{3}}{9-3}\\\\&=\dfrac{2\sqrt{3}}{6}\\\\&\Large \boxed{\sf \bf \ \ =\dfrac{\sqrt{3}}{3} \ \ }\end{aligned}$

p = 0, q = 1/3

Thank you.