GCEMathematicsIndices, Logarithms and Surds2021

Simplify $\frac{5\sqrt{2} + \sqrt{50}}{\sqrt{8}}$.

A5CORRECT
B$5\sqrt{2}$
C$\frac{5\sqrt{2}}{2}$
D10
AI
Toaster Teacher
Why the answer is A, and why the others tempt you.
$\sqrt{50} = 5\sqrt{2}$ and $\sqrt{8} = 2\sqrt{2}$, so the expression becomes $\frac{5\sqrt{2} + 5\sqrt{2}}{2\sqrt{2}} = \frac{10\sqrt{2}}{2\sqrt{2}} = 5$. Errors occur when candidates fail to simplify the surds before operating.
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