simplify.\n10\\sqrt{50}

Explanation:

Step1: Factorize 50

$50 = 25\times2$

Step2: Rewrite the square - root

$10\sqrt{50}=10\sqrt{25\times2}$

Step3: Use the square - root property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 25$, $b = 2$)

$10\sqrt{25\times2}=10\times\sqrt{25}\times\sqrt{2}$

Step4: Evaluate $\sqrt{25}$

Since $\sqrt{25}=5$, then $10\times\sqrt{25}\times\sqrt{2}=10\times5\times\sqrt{2}$

Step5: Calculate the product

$10\times5\times\sqrt{2}=50\sqrt{2}$

Answer:

$50\sqrt{2}$