Question

How do I simplify radicals in simplest radical form?

Answer 1

Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots e.t.c

Examples of radicals are

$\sqrt[]{4},\sqrt[2]{8},\sqrt[3]{16}$

For exmaple,

Given the radical

$\sqrt[]{12}$

To simplify into the simplest radical,

Factorize the perfect square

$\sqrt[]{12}=\sqrt[]{4\times3}$

Then we take out the pairs

$\begin{gathered} \sqrt[]{12}=\sqrt[]{4}\times\sqrt[]{3} \\ \sqrt[]{12}=\sqrt[]{2\times2}\times\sqrt[]{3} \\ \sqrt[]{12}=\sqrt[]{2^2}\times\sqrt[]{3} \end{gathered}$

Simplify the result

$\begin{gathered} \text{Where} \\ \sqrt[]{2^2}=2 \\ \sqrt[]{12}=2\times\sqrt[]{3} \\ \sqrt[]{12}=2\sqrt[]{3} \end{gathered}$

Hence, the simplified radical of the example used is

$\sqrt[]{12}=2\sqrt[]{3}$