Answer:
C. 2√10
Explanation:
Given the product below:
[tex]\sqrt[]{2}\times\sqrt[]{20}[/tex]
First, simplify √20 by expressing 20 as a product of two numbers where one is a perfect square:
[tex]\sqrt[]{20}=\sqrt[]{4\times5}[/tex]
By the multiplication of surds, it is given that:
[tex]\begin{gathered} \sqrt[]{m}\times\sqrt[]{n}=\sqrt[]{mn} \\ \implies\sqrt[]{4\times5}=\sqrt[]{4}\times\sqrt[]{5}=2\times\sqrt[]{5}=2\sqrt[]{5} \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} \sqrt[]{2}\times\sqrt[]{20}=\sqrt[]{2}\times2\sqrt[]{5}=2\times\sqrt[]{2}\times\sqrt[]{5} \\ \text{Applying the multiplication of surds rule stated earlier:} \\ =2\times\sqrt[]{2\times5} \\ =2\times\sqrt[]{10} \\ \implies\sqrt[]{2}\times\sqrt[]{20}=2\sqrt[]{10} \end{gathered}[/tex]
The correct option is C.
