Simplify the following expression to a simplified fraction: √5√80+√8459+√45√5
Let's take the inside first and rationalize the denominator. (note that the outer square root still exists, it's just more convenient this way).
√5(5√80+√8459+√45)√5⋅√5.
Simplifying the fraction gives
5√5√80+659+155
Simplifying the fraction further gives
54+659+155
Doing some basic operations (adding and dividing) gives us
16936
Finally, we finish by applying the outer square root. This gives us
√16936=136,
which is our final answer. The $\LaTeX$ on that one was tough!