Question

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

Answer 1

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


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

Answer 2

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