How do you simplify #-2sqrt3+3sqrt27#?

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Answer 1 · 2017-07-07T22:25:42

See a solution process below:

First, rewrite the expression as:

#-2sqrt(3) + 3sqrt(9 * 3)#

Next, use this rule of radicals to simplify the term on the right:

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

#-2sqrt(3) + 3sqrt(color(red)(9) * color(blue)(3)) => -2sqrt(3) + 3(sqrt(color(red)(9)) * sqrt(color(blue)(3))) =>#

#-2sqrt(3) + 3(3 * sqrt(3)) =>#

#-2sqrt(3) + 9sqrt(3)#

Now, we can factor our the common term giving:

#(-2 + 9)sqrt(3) =>#

#7sqrt(3)#