Q. 241 - Intermediate Algebra

Question

Explain the when a radical expression is in simplest form.

Step-by-Step Solution

Answer

The radical expression is in its simplest form when it cannot be further reduced.

Step 1. Given

To explain when the radical expression is in simplest form.

Step 2. Consider the expression

Consider an expression $\sqrt{27}+4\sqrt{3}$

Simplify this expression,

$\sqrt{27}+4\sqrt{3}=\sqrt{3^2}\sqrt{3}+4\sqrt{3}$

                   $=3\sqrt{3}+4\sqrt{3}$

                   $=7\sqrt{3}$

which is in its simplest form, and it cannot be reduced further.

So the simplest form is the one that cannot be reduced further.