Question

Will all problems adding positive radicals have a rational solution?

Answer 1

Answer:

No

Step-by-step explanation:

Let us consider two positive radicals first,

$\sqrt{3} , \sqrt{5}$

We know that $\sqrt{3}$ is an irrational number and $\sqrt{5}$ 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,

$\sqrt{4}+\sqrt{4}  =4$

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