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

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Answer 1 · 2017-07-30T11:07:25

See a solution process below:

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))#