How do you simplify #-2\sqrt { 80} ( 8\sqrt { 5} - 2)#?

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Answer 1 · 2017-11-23T14:01:23

See a solution process below:

First, rewrite the radical on the left and use this rule for radicals to simplify it:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#-2sqrt(16 * 5)(8sqrt(5) - 2) =>#

#-2sqrt(16)sqrt(5)(8sqrt(5) - 2) =>#

#(-2 * 4)sqrt(5)(8sqrt(5) - 2) =>#

#-8sqrt(5)(8sqrt(5) - 2)#

Next, multiply each term within the parenthesis by the term outside the parenthesis to eliminate the parenthesis:

#color(red)(-8sqrt(5))(8sqrt(5) - 2) =>#

#(color(red)(-8sqrt(5)) xx 8sqrt(5)) - (color(red)(-8sqrt(5)) xx 2) =>#

#(color(red)(-8) xx 8 xx color(red)(sqrt(5)) xx sqrt(5)) - (2 xx color(red)(-8sqrt(5))) =>#

#(-64 xx 5) - (-16sqrt(5)) =>#

#-320 + 16sqrt(5)#