Question

Which of the following is equivalent to the product below?

Answer 1

C. 2√10

Explanation:

Given the product below:

`\sqrt[]{2}*\sqrt[]{20}`

First, simplify √20 by expressing 20 as a product of two numbers where one is a perfect square:

`\sqrt[]{20}=\sqrt[]{4*5}`

By the multiplication of surds, it is given that:

`\begin{gathered} \sqrt[]{m}*\sqrt[]{n}=\sqrt[]{mn} \\ \implies\sqrt[]{4*5}=\sqrt[]{4}*\sqrt[]{5}=2*\sqrt[]{5}=2\sqrt[]{5} \end{gathered}`

Therefore:

`\begin{gathered} \sqrt[]{2}*\sqrt[]{20}=\sqrt[]{2}*2\sqrt[]{5}=2*\sqrt[]{2}*\sqrt[]{5} \\ \text{Applying the multiplication of surds rule stated earlier:} \\ =2*\sqrt[]{2*5} \\ =2*\sqrt[]{10} \\ \implies\sqrt[]{2}*\sqrt[]{20}=2\sqrt[]{10} \end{gathered}`

The correct option is C.