How do you simplify #(-2+sqrt8)/(-3-sqrt2)#?

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Answer 1 · 2015-06-09T21:11:38

Multiply numerator and denominator by #(3-sqrt(2))#, expand, group, combine and eliminate common factors to get:

#(-2+sqrt(8))/(-3-sqrt(2)) = 1-sqrt(2)#

#(-1+sqrt(8))/(-3-sqrt(2))#

#=(1-sqrt(8))/(3+sqrt(2))#

#=(1-sqrt(8))/(3+sqrt(2))*(3-sqrt(2))/(3-sqrt(2))#

#=((1-2sqrt(2))*(3-sqrt(2)))/(3^2-(sqrt(2))^2)#

[using the difference of squares identity: #a^2-b^2 = (a+b)(a-b)#]

#=(3-sqrt(2)-6sqrt(2)+2(sqrt(2))^2)/(9-2)#

#=(3-7sqrt(2)+4)/7#

#=(7-7sqrt(2))/7#

#=1-sqrt(2)#