How do you simplify #6 sqrt3 - 2 sqrt 12#?

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Answer 1 · 2018-03-21T10:29:21

See a solution process below:

First, rewrite the term under the radical on the right as:

#6sqrt(3) - 2sqrt(4 * 3)#

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

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

#6sqrt(3) - 2sqrt(color(red)(4) * color(blue)(3)) =>#

#6sqrt(3) - 2sqrt(color(red)(4))sqrt(color(blue)(3)) =>#

#6sqrt(3) - (2 * 2)sqrt(3) =>#

#6sqrt(3) - 4sqrt(3)#

Now, we can factor out the common term to complete the simplification:

#(6 - 4)sqrt(3) =>#

#2sqrt(3)#