Question

I started the question but got the wrong answer according to the mark scheme. Please help?

Answer 1

I Used A Calculator To Get The Answer....So Hopefully It's Right

Answer 2

$\bf \cfrac{8-\sqrt{18}}{\sqrt{2}}=a+b\sqrt{2}\qquad \qquad 18\to 3\cdot 3\cdot 2\to 3^2\cdot 2\\\\ -----------------------------\\\\ \cfrac{8-\sqrt{3^2\cdot 2}}{\sqrt{2}}\implies \cfrac{8-3\sqrt{2}}{\sqrt{2}}\impliedby \textit{now, let's distribute the denominator} \\\\\\ \cfrac{8}{\sqrt{2}}-\cfrac{3\sqrt{2}}{\sqrt{2}}\implies \boxed{\cfrac{8}{\sqrt{2}}-3}\impliedby \textit{let's rationalize some}\\\\ -----------------------------$

$\bf \cfrac{8}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{8\sqrt{2}}{(\sqrt{2})^2}\implies \cfrac{8\sqrt{2}}{2}\implies 4\sqrt{2}\\\\ -----------------------------\\\\ thus\qquad \cfrac{8}{\sqrt{2}}-3\iff 4\sqrt{2}-3\implies \begin{array}{ccllll} -3&+4&\sqrt{2}\\ \uparrow &\uparrow \\ a&b \end{array}$