How do you simplify #2sqrt3(2sqrt3-4sqrt5)#?

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Answer 1 · 2017-05-26T20:24:27

See a solution process below:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

#color(red)(2sqrt(3))(2sqrt(3) - 4sqrt(5)) =>#

#(color(red)(2sqrt(3)) xx 2sqrt(3)) - (color(red)(2sqrt(3)) xx 4sqrt(5)) =>#

#((2 xx 2)(sqrt(3) xx sqrt(3))) - ((2 xx 4)(sqrt(3) xx sqrt(5))) =>#

#(4 xx 3) - (8(sqrt(3) xx sqrt(5))) =>#

#12 - (8(sqrt(3) xx sqrt(5)))#

We can now use this rule of radicals to simplify the term on the right:

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

#12 - (8(sqrt(color(red)(3)) xx sqrt(color(blue)(5)))) =>#

#12 - (8sqrt(color(red)(3) xx color(blue)(5))) =>#

#12 - 8sqrt(15)#