select the correct answer.\nsimplify.\n$sqrt{75}$\na. $3sqrt{5}$\nb. $15sqrt{5}$\nc. $25sqrt{3}$\nd…

Answer:

D. $5\sqrt{3}$

Explanation:

Step1: Factorize 75

$75 = 25\times3$

Step2: Apply square - root property

$\sqrt{75}=\sqrt{25\times3}$ According to the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 25$, $b = 3$), we have $\sqrt{25\times3}=\sqrt{25}\cdot\sqrt{3}$

Step3: Simplify $\sqrt{25}$

$\sqrt{25}=5$, so $\sqrt{25}\cdot\sqrt{3}=5\sqrt{3}$