How do you simplify \sqrt { \frac { 80} { 3} }√803?

2 Answers
Andy Y.
Dec 19, 2017

=(4sqrt(5))/3=4√53

Explanation:

It is unclear if the radicand includes the 33 or not. Assuming you mean

(sqrt(80))/3√803

Then you have

(sqrt(16*5))/3√16⋅53

=(4sqrt(5))/3=4√53

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

smendyka
Dec 19, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

sqrt(80)/sqrt(3)√80√3

Next, simplify the numerator:

sqrt(80)/sqrt(3) => sqrt(16 * 5)/sqrt(3) => (sqrt(16)sqrt(5))/sqrt(3) => (4sqrt(5))/sqrt(3)√80√3⇒√16⋅5√3⇒√16√5√3⇒4√5√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)) =>4√5√3⇒4√5√3×√3√3⇒4√5√3√3√3⇒

(4sqrt(5 xx 3))/3 => (4sqrt(15))/34√5×33⇒4√153

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