How do you simplify #9sqrt3 - 2sqrt12#?

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Answer 1 · 2018-06-25T13:31:06

See a solution process below:

First, use this rule for radicals to simplify the radical on the right:

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

#9sqrt(3) - 2sqrt(12) =>#

#9sqrt(3) - 2sqrt(color(red)(4) * color(blue)(3)) =>#

#9sqrt(3) - 2sqrt(color(red)(4))sqrt(color(blue)(3)) =>#

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

#9sqrt(3) - 4sqrt(color(blue)(3))#

Now, we can factor out the common term giving:

#9sqrt(color(blue)(3)) - 4sqrt(color(blue)(3)) =>#

#(9 - 4)sqrt(color(blue)(3)) =>#

#5sqrt(3)#