Question

How do you multiply `4\sqrt { 15a } \cdot 4\sqrt { 3a }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`4 * 4 * sqrt(15a)sqrt(3a) =>`

`16sqrt(15a)sqrt(3a)`

Next, use this rule for radicals to combine the radicals:

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

`16sqrt(color(red)(15a)) * sqrt(color(blue)(3a)) =>`

`16sqrt(color(red)(15a) * color(blue)(3a)) =>`

`16sqrt(45a^2)`

Then, rewrite the term in the radical as:

`16sqrt(9a^2 * 5)`

Now, use this rule of radicals to complete the simplification:

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

`16sqrt(color(red)(9a^2) * color(blue)(5)) =>`

`16sqrt(color(red)(9a^2)) * sqrt(color(blue)(5)) =>`

`16 * 3a * sqrt(color(blue)(5)) =>`

`48asqrt(5)`