Question

Given that (in picture)...

Answer 1

Answer:  a = -3 and b = 5

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Work Shown:

Multiply top and bottom by $\sqrt{2}$ to rationalize the denominator

$\frac{10-\sqrt{18}}{\sqrt{2}}\\\\\frac{\sqrt{2}(10-\sqrt{18})}{\sqrt{2}*\sqrt{2}}\\\\\frac{\sqrt{2}*10-\sqrt{2}*\sqrt{18}}{\sqrt{2*2}}\\\\\frac{\sqrt{2}*10-\sqrt{2*18}}{\sqrt{4}}\\\\\frac{10\sqrt{2}-\sqrt{36}}{2}\\\\\frac{10\sqrt{2}-6}{2}\\\\\frac{-6+10\sqrt{2}}{2}\\\\\frac{2(-3+5\sqrt{2})}{2}\\\\-3+5\sqrt{2}$

We end up with something in the form $a+b\sqrt{2}$ where a = -3 and b = 5