Question

What is the product of 3√6 and 5√12 in simplest radical form?

Answer 1

In order to calculate and simplify this product, we need to use the following properties:

`\begin{gathered} \sqrt[]{a}\cdot\sqrt[]{b}=\sqrt[]{a\cdot b} \\ \sqrt[c]{a^b}=a\sqrt[c]{a^(b-c)} \end{gathered}`

So we have that:

`\begin{gathered} 3\sqrt[]{6}\cdot5\sqrt[]{12} \\ =(3\cdot5)\cdot(\sqrt[]{6}\cdot\sqrt[]{2\cdot6}) \\ =15\cdot\sqrt[]{2\cdot6^2} \\ =15\cdot6\cdot\sqrt[]{2} \\ =90\sqrt[]{2} \end{gathered}`

So the result in the simplest radical form is 90√2.