Simplify this Radical Expression...?

Question

I want to simplify 2 sqrt5 / (sqrt2 +5)

I'm not sure what to do with the ()s.
Please help.

Answer 1

2 sqrt(5)/ (sqrt(2) +5)
(2 sqrt(5)/ (sqrt(2) +5))*((sqrt(2) -5)/(sqrt(2) -5))
(2sqrt(10)-10sqrt(5))/(2-25)
(2sqrt(10)-10sqrt(5))//-23

Answer 2

2 sqrt5 / (sqrt2 +5)
multiply top and bottom by sqrt2-5
2sqrt5(sqrt2-5) / (sqrt2+5)(sqrt2-5) =
2(sqrt10 - 5sqrt5) / (2-25) =
(10sqrt5 - 2sqrt10) / 23

Did you mean
(2- sqrt5) / (sqrt2 +5)
If so, you still multiply top and bottom by (sqrt2 - 5) to get rid of the radical in the denominator.

Simplest form never has a radical in the denominator. Simplest form also never has a negative number in the denominator, which is why I show the answer as (10sqrt5 - 2sqrt10) / 23
and not (2sqrt10 - 10sqrt5) / (-23)

Answer 3

Simplifying a radical expression means not having any radical (square root) in the denominator. The ()'s don't make a difference with this problem, but they do remind you that you should multiple by the opposite binomial to get the difference of two squares which eliminates the middle term, or, in this case, the term with the square root.