Question

How do you multiply `\sqrt { 7x ^ { 5} } \cdot \sqrt { 35x }`?

Answer 1

See a solution process below:

Explanation:

We can use this rule of radicals to multiply these two terms:

`sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))`

`sqrt(color(red)(7x^5)) * sqrt(color(blue)(35x)) => sqrt(color(red)(7x^5) * color(blue)(35x)) => sqrt(245x^6)`

We can simplify this as:

`sqrt(245x^6) => sqrt(color(red)(49x^6) * color(blue)(5)) => sqrt(color(red)(49x^6)) * sqrt(color(blue)(5)) => 7x^3sqrt(5)`