How do you rationalize the denominator and simplify 15+3√37+√8?

1 Answer
smendyka
Jun 18, 2017

See a solution process below:

Explanation:

To rationalize the denominator, multiply the fraction by 1 in the form of: 7−√87−√8:

7−√87−√8×15+3√37+√8⇒

(7⋅15)+(7⋅3√3)−15√8−3√8√3(7⋅7)+7√8−7√8−(√8)2⇒

105+21√3−15√8−3√8⋅349+(7√8−7√8)−8⇒

105+21√3−15√8−3√2441⇒

105+21√3−15√8−3√4⋅641⇒

105+21√3−15√8−3√4√641⇒

105+21√3−15√8−(3⋅2√6)41⇒

105+21√3−15√8−6√641

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