Question

How do you simplify `5sqrt(3x^3)+2sqrt(27x)`?

Answer 1

See a solution process below:

Explanation:

Step 1) Simplify the radicals by rewriting the radicals and then using this rule for radicals:

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

`5sqrt(color(red)(x^2) * color(blue)(3x)) + 2sqrt(color(red)(9) * color(blue)(3x)) =>`

`5sqrt(color(red)(x^2))sqrt(color(blue)(3x)) + 2sqrt(color(red)(9))sqrt(color(blue)(3x)) =>`

`5xsqrt(color(blue)(3x)) + (2 * 3)sqrt(color(blue)(3x)) =>`

`5xsqrt(color(blue)(3x)) + 6sqrt(color(blue)(3x))`

Step 2) Combine like terms by factoring out the common term: `sqrt(color(blue)(3x))` :

`(5x + 6)sqrt(color(blue)(3x))`