How do you simplify $\sqrt{\frac{80}{3}}$ $\sqrt { \frac { 80} { 3} }$ ?

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How do you simplify $\sqrt{\frac{80}{3}}$ $\sqrt { \frac { 80} { 3} }$ ?

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Answer 1 · 2017-12-19T17:49:04

$= \frac{4 \sqrt{5}}{3}$ $=(4sqrt(5))/3$

Explanation:

It is unclear if the radicand includes the $3$ $3$ or not. Assuming you mean

$\frac{\sqrt{80}}{3}$ $(sqrt(80))/3$

Then you have

$\frac{\sqrt{16 \cdot 5}}{3}$ $(sqrt(16*5))/3$

$= \frac{4 \sqrt{5}}{3}$ $=(4sqrt(5))/3$

This does not simplify any further and thus is the final answer.

Answer 2 · 2017-12-19T17:51:26

See a solution process below:

Explanation:

First, rewrite the expression as:

$\frac{\sqrt{80}}{\sqrt{3}}$ $sqrt(80)/sqrt(3)$

Next, simplify the numerator:

$\frac{\sqrt{80}}{\sqrt{3}} \Rightarrow \frac{\sqrt{16 \cdot 5}}{\sqrt{3}} \Rightarrow \frac{\sqrt{16} \sqrt{5}}{\sqrt{3}} \Rightarrow \frac{4 \sqrt{5}}{\sqrt{3}}$ $sqrt(80)/sqrt(3) => sqrt(16 * 5)/sqrt(3) => (sqrt(16)sqrt(5))/sqrt(3) => (4sqrt(5))/sqrt(3)$

Now, we can rationalize the denominator:

$\frac{4 \sqrt{5}}{\sqrt{3}} \Rightarrow \frac{4 \sqrt{5}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \Rightarrow \frac{4 \sqrt{5} \sqrt{3}}{\sqrt{3} \sqrt{3}} \Rightarrow$ $(4sqrt(5))/sqrt(3) => (4sqrt(5))/sqrt(3) xx sqrt(3)/sqrt(3) => (4sqrt(5)sqrt(3))/(sqrt(3)sqrt(3)) =>$

$\frac{4 \sqrt{5 \times 3}}{3} \Rightarrow \frac{4 \sqrt{15}}{3}$ $(4sqrt(5 xx 3))/3 => (4sqrt(15))/3$

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