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

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Answer 1 · 2017-12-19T17:49:04

$=(4sqrt(5))/3$

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.

Answer 2 · 2017-12-19T17:51:26

See a solution process below:

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:

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

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

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