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)#