How do you multiply #(\sqrt { 3} + \sqrt { 2} ) ( \sqrt { 4} + 2\sqrt { 2} )#?

1 Answer
smendyka
Jul 22, 2017

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(sqrt(3)) + color(red)(sqrt(2)))(color(blue)(sqrt(4)) + color(blue)(2sqrt(2))) =>#

#(color(red)(sqrt(3)) + color(red)(sqrt(2)))(color(blue)(2) + color(blue)(2sqrt(2))) =>#becomes:

#(color(red)(sqrt(3)) xx color(blue)(2)) + (color(red)(sqrt(3)) xx color(blue)(2sqrt(2))) + (color(red)(sqrt(2)) xx color(blue)(2)) + (color(red)(sqrt(2)) xx color(blue)(2sqrt(2)))#

#2sqrt(3) + 2sqrt(3)sqrt(2) + 2sqrt(2) + 2sqrt(2)sqrt(2) =>#

#2sqrt(3) + 2sqrt(3 * 2) + 2sqrt(2) + 2sqrt(2 * 2) =>#

#2sqrt(3) + 2sqrt(6) + 2sqrt(2) + 2sqrt(4) =>#

#2sqrt(3) + 2sqrt(6) + 2sqrt(2) + (2 * 2) =>#

#2sqrt(3) + 2sqrt(6) + 2sqrt(2) + 4#

If necessary, we can now factor out like terms:

#2(sqrt(3) + sqrt(6) + sqrt(2)) + 4 =>#

#2(sqrt(6) + sqrt(3) + sqrt(2)) + 4 =>#

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