How do you simplify #-sqrt45+2sqrt5-sqrt20-2sqrt6#?

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Answer 1 · 2017-05-10T13:24:43

See a solution process below:

First, we can use this rule of radicals to simplify two of the terms:

#sqrt(a * b) = sqrt(a) * sqrt(b)#

#-color(red)(sqrt(45)) + 2sqrt(5) - color(red)(sqrt(20)) - 2sqrt(6) =>#

#-color(red)(sqrt(9 * 5)) + 2sqrt(5) - color(red)(sqrt(4 * 5)) - 2sqrt(6) =>#

#-(color(red)(sqrt(9)) * color(red)(sqrt(5))) + 2sqrt(5) - (color(red)(sqrt(4)) * color(red)(sqrt(5))) - 2sqrt(6) =>#

#-(3color(red)(sqrt(5))) + 2sqrt(5) - (2color(red)(sqrt(5))) - 2sqrt(6) =>#

#-3sqrt(5) + 2sqrt(5) - 2sqrt(5) - 2sqrt(6)#

We can now combine like terms:

#-3sqrt(5) + (2 - 2)sqrt(5) - 2sqrt(6) =>#

#-3sqrt(5) + (0 * sqrt(5)) - 2sqrt(6) =>#

#-3sqrt(5) - 2sqrt(6) =>#