How do you simplify $(sqrt3 - sqrt5) (sqrt5 + sqrt7)$ ?

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Answer 1 · 2017-08-14T09:10:08

$sqrt15+sqrt21-5-sqrt35$

Use the foil method:
$(a+b)(c+d)=ac+ad+bc+bd$
$sqrt15+sqrt21-5-sqrt35$

Answer 2 · 2017-08-14T09:11:59

$-5+sqrt(15)+sqrt(21)-sqrt(35)$

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

$=sqrt(3)*sqrt(5)+sqrt(3)*sqrt(7)-sqrt(5)*sqrt(5)-sqrt(5)sqrt(7)$

because
$sqrt(a)*sqrt(b)=sqrt(ab)$

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

$=-5+sqrt(15)+sqrt(21)-sqrt(35)$

How do you simplify (sqrt3 - sqrt5) (sqrt5 + sqrt7) (sqrt3 - sqrt5) (sqrt5 + sqrt7)?