Answer: a = -3 and b = 5
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Work Shown:
Multiply top and bottom by [tex]\sqrt{2}[/tex] to rationalize the denominator
[tex]\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}\\\\[/tex]
We end up with something in the form [tex]a+b\sqrt{2}[/tex] where a = -3 and b = 5
