Answer
See explanations.
Work Step by Step
Step 1. Using the formula $\sqrt a\sqrt b=\sqrt {ab}$, we have $\sqrt {10}\sqrt 5=\sqrt {10\cdot 5}$
Step 2. Factor to get $\sqrt {10\cdot 5}=\sqrt {2\cdot5\cdot 5}$
Step 3. Using the formula $\sqrt {a\cdot a}=\sqrt {a^2}=|a|$, we have $\sqrt {2\cdot5\cdot 5}=\sqrt 2\sqrt {5\cdot 5}=5\sqrt 2$
