How do you evaluate #(\sqrt { 2} - \sqrt { 17} ) ( \sqrt { 15} - \sqrt { 7} )#?

1 Answer
smendyka
May 4, 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(2)) - color(red)(sqrt(17)))(color(blue)(sqrt(15)) - color(blue)(sqrt(7)))# becomes:

#(color(red)(sqrt(2)) xx color(blue)(sqrt(15))) - (color(red)(sqrt(2)) xx color(blue)(sqrt(7))) - (color(red)(sqrt(17)) xx color(blue)(sqrt(15))) + (color(red)(sqrt(17)) xx color(blue)(sqrt(7)))#

We can use this rule for multiplying radicals to simplify the expression:

#sqrt(color(red)(2) xx color(blue)(15)) - sqrt(color(red)(2) xx color(blue)(7)) - sqrt(color(red)(17) xx color(blue)(15)) + sqrt(color(red)(17) xx color(blue)(7)) =>#

#sqrt(30) - sqrt(14) - sqrt(255) + sqrt(119)#

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