simplify.\n10\\sqrt{8}

Explanation:

Step1: Factorize the number inside square - root

We know that $8 = 4\times2$, so $10\sqrt{8}=10\sqrt{4\times2}$.

Step2: Use the property of square - roots $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 4$, $b = 2$)

$10\sqrt{4\times2}=10\times\sqrt{4}\times\sqrt{2}$. Since $\sqrt{4}=2$, then $10\times\sqrt{4}\times\sqrt{2}=10\times2\times\sqrt{2}$.

Step3: Perform the multiplication

$10\times2\times\sqrt{2}=20\sqrt{2}$.

Answer:

$20\sqrt{2}$