How do you simplify #(sqrt3 -sqrt6)/(sqrt3 +sqrt 6)#?

1 Answer

Answer:

#-3+2sqrt2#

Explanation:

We can rationalize the denominator by remembering that:

#(sqrta+sqrtb)(sqrta-sqrtb)=a-b#

In this case:

#(sqrt3-sqrt6)/(sqrt3+sqrt6)#

#(sqrt3-sqrt6)/(sqrt3+sqrt6)(1)#

#(sqrt3-sqrt6)/(sqrt3+sqrt6)((sqrt3-sqrt6)/(sqrt3-sqrt6))#

#(sqrt3-sqrt6)^2/(3-6)#

#(3+6-2sqrt18)/(-3)#

#(9-6sqrt2)/(-3)=-3+2sqrt2#