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

2 Answers
Dec 19, 2017

=(4sqrt(5))/3

Explanation:

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

(sqrt(80))/3

Then you have

(sqrt(16*5))/3

=(4sqrt(5))/3

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

Dec 19, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

sqrt(80)/sqrt(3)

Next, simplify the numerator:

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:

(4sqrt(5))/sqrt(3) => (4sqrt(5))/sqrt(3) xx sqrt(3)/sqrt(3) => (4sqrt(5)sqrt(3))/(sqrt(3)sqrt(3)) =>

(4sqrt(5 xx 3))/3 => (4sqrt(15))/3