Question

How do you multiply `\sqrt { 2f ^ { 4} } \cdot \sqrt { 45f ^ { 2} }`?

Answer 1

See a solution process below:

Explanation:

First, use this rule of radicals to multiply the radicals:

`sqrt(color(red)(2f^4)) * sqrt(color(blue)(45f^2)) = sqrt(color(red)(2f^4) * color(blue)(45f^2)) = sqrt((2 * 45) * (f^4 * f^2)) =`

`sqrt(90f^6)`

We can now use this rule for multiplying radicals in reverse to simplify this expression as:

`sqrt(9f^6 * 10) = sqrt(9f^6) * sqrt(10) = 3f^3sqrt(10)`