Answer:
No
Step-by-step explanation:
Let us consider two positive radicals first,
[tex]\sqrt{3} , \sqrt{5}[/tex]
We know that [tex]\sqrt{3}[/tex] is an irrational number and [tex]\sqrt{5}[/tex] is also an irrational number.
So the sum of two positive radicals does not always have a rational solution.
There are examples when the some of adding positive radicals can get us a rational solution. For example,
[tex]\sqrt{4}+\sqrt{4} =4[/tex]
So if the radicand is a perfect square then the solution is rational.
