How do you simplify #sqrt11 (sqrt6 - sqrt7)#?

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Answer 1 · 2017-11-14T13:08:17

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)(sqrt(11))(sqrt(6) - sqrt(7)) =>#

#(color(red)(sqrt(11)) xx sqrt(6)) - (color(red)(sqrt(11)) xx sqrt(7))#

Now, use this rule for radicals to combine the radicals within the parenthesis:

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

#(sqrt(color(red)(11)) * sqrt(color(blue)(6))) - (sqrt(color(red)(11)) * sqrt(color(blue)(7))) =>#

#sqrt(color(red)(11) * color(blue)(6)) - sqrt(color(red)(11) * color(blue)(7)) =>#

#sqrt(66) - sqrt(77)#