How do you evaluate #-\sqrt { 2} ( \sqrt { 6} + 4)#?

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Answer 1 · 2017-08-13T14:31:43

See a solution process below:

First, multiply each term within the parenthesis by the term outside the parenthesis to expand the expression:

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

#color(red)(-sqrt(2))sqrt(6) - 4color(red)(sqrt(2))#

Then, combine the radicals and simplify:

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

#-sqrt(12) - 4sqrt(2) =>#

#-sqrt(4 * 3) - 4sqrt(2) =>#

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

#-2sqrt(3) - 4sqrt(2)#

If required, the single number this expression evaluates to is:

(-2 * 1.732) - (4 * 1.414) =>#

#-3.464 - 5.657 =>#

#-9.121# rounded to the nearest thousandth.