Simplify.
-$\frac{\sqrt{5 t^{11}}}{\sqrt{80 t^{5}}}$
A) $\sqrt{\frac{t^{3}}{4}}$
B) $\frac{t^{6}}{4}$
C) $\frac{t^{3}}{4}$
D) $\frac{t^{3}}{\sqrt{4}}$

Question

Quizplus · Accepted Answer

First, simplify the expression inside the square root by dividing both the numerator and the denominator by their greatest common divisor and simplifying the powers of $t$: $\frac{\sqrt{5 t^{11}}}{\sqrt{80 t^{5}}} = \sqrt{\frac{5t^{11}}{80t^{5}}} = \sqrt{\frac{t^{6}}{16}} = \sqrt{\frac{t^{6}}{4^2}}$. This simplifies further to $\frac{t^{3}}{4}$, since taking the square root of $t^{6}$ results in $t^{3}$ and the square root of $4^2$ is 4.

Simplify - 5t1180t5\frac{\sqrt{5 t^{11}}}{\sqrt{80 t^{5}}}80t5​5t11​​ A) t34\sqrt{\frac{t^{3}}{4}}4t3​​ B) t64\frac{t^{6}}{4}4t6​ C) t34\frac{t^{3}}{4}4t3​ D) t34\frac{t^{3}}{\sqrt{4}}4​t3​

Simplify
- $\frac{\sqrt{5 t^{11}}}{\sqrt{80 t^{5}}}$ A) $\sqrt{\frac{t^{3}}{4}}$ B) $\frac{t^{6}}{4}$ C) $\frac{t^{3}}{4}$ D) $\frac{t^{3}}{\sqrt{4}}$