Answer
$10+7\sqrt{2}$
Work Step by Step
Distribute $\sqrt2$:
$\sqrt{2}(\sqrt{50}+7)$
$=\sqrt{2}\sqrt{50}+\sqrt{2} \cdot 7$
Recall the property (pg. 367):
$\sqrt[n]{a}\cdot \sqrt[n]{b}=\sqrt[n]{ab}$ (if $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers)
Applying this property, we get:
$=\sqrt{2\cdot50}+\sqrt{2}\cdot7$
$=\sqrt{100}+\sqrt{2}\cdot7$
$=10+7\sqrt{2}$ (because $10^2=100$)