How do you simplify (sqrt3 - sqrt5) (sqrt5 + sqrt7)(√3−√5)(√5+√7)?

2 Answers
Austte
Aug 14, 2017

sqrt15+sqrt21-5-sqrt35√15+√21−5−√35

Explanation:

Use the foil method:
(a+b)(c+d)=ac+ad+bc+bd(a+b)(c+d)=ac+ad+bc+bd
sqrt15+sqrt21-5-sqrt35√15+√21−5−√35

Andrew
Aug 14, 2017

-5+sqrt(15)+sqrt(21)-sqrt(35)−5+√15+√21−√35

Explanation:

you can distribute out the brackets and simplify it
(sqrt(3)-sqrt(5))(sqrt(5)+sqrt(7))(√3−√5)(√5+√7)

=sqrt(3)*sqrt(5)+sqrt(3)*sqrt(7)-sqrt(5)*sqrt(5)-sqrt(5)sqrt(7)=√3⋅√5+√3⋅√7−√5⋅√5−√5√7

because
sqrt(a)*sqrt(b)=sqrt(ab)√a⋅√b=√ab

Our equation becomes
=sqrt(15)+sqrt(21)-sqrt(25)-sqrt(35)=√15+√21−√25−√35

=-5+sqrt(15)+sqrt(21)-sqrt(35)=−5+√15+√21−√35

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