Question

Will all problems adding positive radicals have a rational solution?

Answer 1

No

Explanation:

Let us consider two positive radicals first,

`√(3) , √(5)`

We know that
`√(3)` is an irrational number and
`√(5)` 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,

`√(4)+√(4)  =4`

So if the radicand is a perfect square then the solution is rational.