simplify.\n5\\sqrt{75}

Explanation:

Step1: Factorize 75

$75 = 25\times3$

Step2: Rewrite the square - root

$5\sqrt{75}=5\sqrt{25\times3}$

Step3: Use the square - root property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 25$, $b = 3$)

$5\sqrt{25\times3}=5\times\sqrt{25}\times\sqrt{3}$

Step4: Evaluate $\sqrt{25}$

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

Step5: Calculate the product

$5\times5\times\sqrt{3}=25\sqrt{3}$

Answer:

$25\sqrt{3}$