How do you simplify #3sqrt12+ 4sqrt18#?

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Answer 1 · 2018-03-08T19:48:17

See a solution process below:

First, rewrite each radical as:

#3sqrt(4 * 3) + 4sqrt(9 * 2)#

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

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

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

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

#(3 * 2)sqrt(color(blue)(3)) + (4 * 3)sqrt(color(blue)(2)) =>#

#6sqrt(3) + 12sqrt(2)#

Or

#6(sqrt(3) + 2sqrt(2))#