How do you simplify #(sqrt12 - 4 ) - ( 8 + sqrt27 )#?

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Answer 1 · 2018-03-04T22:02:53

See a solution process below:

First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

#sqrt(12) - 4 - 8 - sqrt(27)#

Next, group like terms:

#sqrt(12) - sqrt(27) - 4 - 8#

Then, combine like terms:

#sqrt(12) - sqrt(27) - 12#

Now, use this rule of radicals to simplify and combine the radicals:

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

#sqrt(color(red)(4) * color(blue)(3)) - sqrt(color(red)(9) * color(blue)(3)) - 12#

#sqrt(color(red)(4))sqrt(color(blue)(3)) - sqrt(color(red)(9))sqrt(color(blue)(3)) - 12#

#2sqrt(color(blue)(3)) - 3sqrt(color(blue)(3)) - 12#

#(2 - 3)sqrt(color(blue)(3)) - 12#

#-1sqrt(color(blue)(3)) - 12#

#-sqrt(color(blue)(3)) - 12#

Or

#-12 - sqrt(color(blue)(3))#