How do you evaluate #(\sqrt { 3} - 5\sqrt { 10} ) ( 5\sqrt { 10} - 2\sqrt { 3} )#?

1 Answer
smendyka
Jan 30, 2018

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)(5sqrt(10)))(color(blue)(5sqrt(10)) - color(blue)(2sqrt(3)))# becomes:

#(color(red)(sqrt(3)) xx color(blue)(5sqrt(10))) - (color(red)(sqrt(3)) xx color(blue)(2sqrt(3))) - (color(red)(5sqrt(10)) xx color(blue)(5sqrt(10))) + (color(red)(5sqrt(10)) xx color(blue)(2sqrt(3)))#

#5sqrt(3)sqrt(10) - 2sqrt(3)sqrt(3) - 25sqrt(10)sqrt(10) + 10sqrt(10)sqrt(3)#

#5sqrt(3 * 10) - (2 * 3) - (25 * 10) + 10sqrt(10 * 3)#

#5sqrt(30) - 6 - 250 + 10sqrt(30)#

We can now group and combine like terms:

#5sqrt(30) + 10sqrt(30) - 6 - 250#

#(5 + 10)sqrt(30) - 256#

#15sqrt(30) - 256#

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