what is the simplified form of $sqrt{\frac{2160x^{8}}{60x^{2}}}$? assume $x\neq0$.\n$36x^{3}$\n$36x^{2}$\n$6x…

Answer:

C. $6x^{3}$

Explanation:

Step1: Simplify the fraction inside the square - root

First, simplify $\frac{2160x^{8}}{60x^{2}}$. Divide the coefficients and use the quotient - rule of exponents $a^{m}\div a^{n}=a^{m - n}$. The coefficient $\frac{2160}{60}=36$, and for the variable part $x^{8}\div x^{2}=x^{8 - 2}=x^{6}$. So, $\frac{2160x^{8}}{60x^{2}} = 36x^{6}$.

Step2: Take the square - root

We know that $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ for $a = 36$ and $b=x^{6}$. $\sqrt{36}=6$ and $\sqrt{x^{6}}=x^{3}$ (since $\sqrt{x^{n}}=x^{\frac{n}{2}}$ and when $n = 6$, $\frac{n}{2}=3$). So, $\sqrt{36x^{6}}=6x^{3}$.