Need Help With Surds/Algebra Questions

[Inertia_Squared]

(this is my first post in this forum so if I've posted in the wrong area or need to provide any more information etc. please feel free to correct me)

I'm a yr 10 student at school and I have 1/2 yearly exams coming up this week and I'm having troubles with two study questions as I cannot recall how to solve these or if my attempted answers are correct at all (they're probably not).

I was wondering if anyone would know the solutions and explain to me how to best solve these in general and under exam conditions if applicable, thanks!

 

[pka]

While this is true
\(\displaystyle \begin{align*}\frac{2}{2+\sqrt{3}}&=\frac{2(2-\sqrt{3})}{4-3} \\&=4-2\sqrt{3}\\&=4-\sqrt{12} \end{align*}\)

so \(\displaystyle a=4~\&~b=12\)

 

[Inertia_Squared]

While this is true
\(\displaystyle \begin{align*}\frac{2}{2+\sqrt{3}}&=\frac{2(2-\sqrt{3})}{4-3} \\&=4-2\sqrt{3}\\&=4-\sqrt{12} \end{align*}\)

so \(\displaystyle a=4~\&~b=12\)

Thanks so much, I can't believe I didn't think of that!

 

[Harry_the_cat]

You have Q10 correct. Well done! And good luck in your exam.

 

[Inertia_Squared]

You have Q10 correct. Well done! And good luck in your exam.

Thanks, I really appreciate all the help!