How do we know if a radical expression is in its simplest form?

Question

mathmale · Answer

The first thing that comes to mind is that there'd be no perfect squares left under the radical sign when we're talking about square roots, no perfect cubes left when we're talking about cube roots, and so on).

For example:  were I to give you the square root of 98, the proper thing to do first would be  to look for perfect square(s) under the radical sign and to factor the radicand (the number under the radical sign) so that all perfect squares are obvious.  Take the square root of each of those and write the results as factors outside and in front of the radical sign.

$$\sqrt{98}=\sqrt{49*2}=\sqrt{49}*\sqrt{2}=7\sqrt{2}$$

mathmale · Answer

Sqrt(2) cannot be reduced further.

anonymous · Answer

Oh!
Thank you.

mathmale · Answer

Dear Burning:  My pleasure.  Good luck!  Try practicing this concept!