How do you simplify #5/(sqrt6+sqrt3)#?

1 Answer
Aug 6, 2017

Answer:

See a solution process below below:

Explanation:

To simplify this we can rationalize the denominator. Or, in other words, remove the radicals from the denominator.

To remove the radicals we need to multiply by the appropriate form of #1#. Remember that #(color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - color(blue)(y)^2# we can multiply this expression as:

#(sqrt(6) - sqrt(3))/(sqrt(6) - sqrt(3)) xx 5/(sqrt(6) + sqrt(3)) =>#

#(5(sqrt(6) - sqrt(3)))/((sqrt(6))^2 - (sqrt(3))^2) =>#

#(5(sqrt(6) - sqrt(3)))/(6 - 3) =>#

#(5(sqrt(6) - sqrt(3)))/3#

Or

#5/3(sqrt(6) - sqrt(3))#