simplify.\n10\\sqrt{75}

Explanation:

Step1: Factorize the number inside square - root

We know that $75 = 25\times3$. So, $10\sqrt{75}=10\sqrt{25\times3}$.

Step2: Use the square - root property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 25$, $b = 3$)

$10\sqrt{25\times3}=10\times\sqrt{25}\times\sqrt{3}$. Since $\sqrt{25}=5$, then $10\times\sqrt{25}\times\sqrt{3}=10\times5\times\sqrt{3}$.

Step3: Perform the multiplication

$10\times5\times\sqrt{3}=50\sqrt{3}$.

Answer:

$50\sqrt{3}$