How do you simplify $(4) / ( sqrt(5)+sqrt(5) )$ ?

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Answer 1 · 2015-10-16T23:27:50

$(2sqrt(5))/5$

Your starting expression is

$4/(sqrt(5) + sqrt(5))$

Notice that you can combine the two radical terms in the denominator to get

$sqrt(5) + sqrt(5) = sqrt(5) * (1 + 1) = 2sqrt(5)$

The expression becomes

$4/(2sqrt(5)) = 2/sqrt(5)$

Next, rationalize the denominator by multiplyg the fraction by $1 = sqrt(5)/sqrt(5)$ . This will get you

$2/sqrt(5) * sqrt(5)/sqrt(5) = (2sqrt(5))/(sqrt(5) * sqrt(5)) = color(green)((2sqrt(5))/5)$

How do you simplify (4) / ( sqrt(5)+sqrt(5) ) (4) / ( sqrt(5)+sqrt(5) )?