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

Question

Avery Alexander · Accepted Answer

See a solution process below:

First, take every term out of parenthesis, paying close attention to the proper handling of each term's sign: #sqrt(12) - 4 - 8 - sqrt(27)# Next, terms that belong to groups: #sqrt(12) - sqrt(27) - 4 - 8# Next, merge similar terms: #sqrt(12) - sqrt(27) - 12# Now, combine and simplify the radicals using this radicals rule: #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))#

Julia Adams · Answer

undefined To simplify the expression (sqrt12 - 4) - (8 + sqrt27), we can first simplify the square roots. The square root of 12 can be simplified as 2√3, and the square root of 27 can be simplified as 3√3.

Now, we can substitute these simplified values back into the expression: (2√3 - 4) - (8 + 3√3).

Next, we can combine like terms within each set of parentheses: 2√3 - 4 - 8 - 3√3.

Combining like terms, we have: -4 - 8 + 2√3 - 3√3.

Simplifying further, we get: -12 - √3.

Therefore, the simplified expression is -12 - √3.