simplify. assume n is greater than or equal to zero. $sqrt{75n^{7}}$

Explanation:

Step1: Factor 75

$75 = 25\times3$, so $\sqrt{75n^{7}}=\sqrt{25\times3\times n^{6}\times n}$.

Step2: Apply square - root property

$\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a = 25n^{6}$, $b = 3n$), then $\sqrt{25\times3\times n^{6}\times n}=\sqrt{25n^{6}}\times\sqrt{3n}$.

Step3: Simplify $\sqrt{25n^{6}}$

$\sqrt{25n^{6}} = 5n^{3}$ since $\sqrt{25}=5$ and $\sqrt{n^{6}}=n^{3}$.

Answer:

$5n^{3}\sqrt{3n}$