How do you simplify √3+3√52√8?

1 Answer
smendyka
Jul 24, 2017

See a solution process below:

Explanation:

First, we need to rationalize the denominator by multiplying the expression by the appropriate form of 1 to eliminate the radical in the denominator:

√8√8⋅√3+3√52√8⇒√8(√3+3√5)2√8√8⇒

√8√3+3√8√52⋅8⇒√8√3+3√8√516

Next, we can use this rule for radicals to simplify the numerator:

√a⋅√b=√a⋅b

√8√3+3√8√516⇒√8⋅3+3√8⋅516⇒

√24+3√4016

We can rewrite this expression as:

√4⋅6+3√4⋅1016

And use this rule for radicals (the opposite of the rule above) to further simplify the expression:

√a⋅b=√a⋅√b

√4⋅6+3√4⋅1016⇒√4√6+3√4√1016⇒

2√6+(3⋅2√10)16⇒2(√6+3√10)16⇒

√6+3√108

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
1839 views around the world
You can reuse this answer
Creative Commons License