How do you evaluate #-2\sqrt { 8} - 2\sqrt { 27} - 2\sqrt { 8} + 2\sqrt { 2}#?

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Answer 1 · 2017-11-29T06:37:45

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

We are given the radical expression

#-2 sqrt(8) - 2 sqrt(27) - 2 sqrt(8) + 2 sqrt(2)#

We will write the above expression as follows:

#-2 sqrt(2*2*2) - 2 sqrt(3*3*3) - 2 sqrt(2*2*2*) + 2 sqrt(2)#

The above expression can be simplified as follows:

#-2*2* sqrt(2) - 2*3 sqrt(3) - 2*2 sqrt(2) + 2 sqrt(2)#

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

We can group "like terms" together to simplify:

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

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

#= - 6*[ sqrt(2) + sqrt(3)]# This is our simplified answer.