How do you simplify (2 sqrt(7) + sqrt(3)) times (3 sqrt(7) - sqrt(2))(2√7+√3)×(3√7−√2)?

1 Answer
Daniel L.
Sep 4, 2016

The value is 42-2sqrt(14)+3sqrt(21)-sqrt(6)42−2√14+3√21−√6

Explanation:

(2sqrt(7)+sqrt(3))xx(3sqrt(7)-sqrt(2))(2√7+√3)×(3√7−√2)
=6*7-2sqrt(7)sqrt(2)+3sqrt(7)sqrt(3)-sqrt(2)sqrt(3)=6⋅7−2√7√2+3√7√3−√2√3
=42-2sqrt(14)+3sqrt(21)-sqrt(6)=42−2√14+3√21−√6

In these calculations I used the following properties of square roots:

  1. sqrt(a*b)=sqrt(a)*sqrt(b)√a⋅b=√a⋅√b

  2. sqrt(a*a)=a√a⋅a=a

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
7460 views around the world
You can reuse this answer
Creative Commons License