How do you simplify $(\sqrt{3} - \sqrt{5}) (\sqrt{5} + \sqrt{7})$ $(sqrt3 - sqrt5) (sqrt5 + sqrt7)$ ?

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How do you simplify $(\sqrt{3} - \sqrt{5}) (\sqrt{5} + \sqrt{7})$ $(sqrt3 - sqrt5) (sqrt5 + sqrt7)$ ?

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Answer 1 · 2017-08-14T09:10:08

$\sqrt{15} + \sqrt{21} - 5 - \sqrt{35}$ $sqrt15+sqrt21-5-sqrt35$

Explanation:

Use the foil method:
$(a + b) (c + d) = a c + a d + b c + b d$ $(a+b)(c+d)=ac+ad+bc+bd$
$\sqrt{15} + \sqrt{21} - 5 - \sqrt{35}$ $sqrt15+sqrt21-5-sqrt35$

Answer 2 · 2017-08-14T09:11:59

$- 5 + \sqrt{15} + \sqrt{21} - \sqrt{35}$ $-5+sqrt(15)+sqrt(21)-sqrt(35)$

Explanation:

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

$= \sqrt{3} \cdot \sqrt{5} + \sqrt{3} \cdot \sqrt{7} - \sqrt{5} \cdot \sqrt{5} - \sqrt{5} \sqrt{7}$ $=sqrt(3)*sqrt(5)+sqrt(3)*sqrt(7)-sqrt(5)*sqrt(5)-sqrt(5)sqrt(7)$

because
$\sqrt{a} \cdot \sqrt{b} = \sqrt{a b}$ $sqrt(a)*sqrt(b)=sqrt(ab)$

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

$= - 5 + \sqrt{15} + \sqrt{21} - \sqrt{35}$ $=-5+sqrt(15)+sqrt(21)-sqrt(35)$

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How do you simplify $(\sqrt{3} - \sqrt{5}) (\sqrt{5} + \sqrt{7})$ $(sqrt3 - sqrt5) (sqrt5 + sqrt7)$ ?

2 Answers

Explanation:

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

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How do you simplify $(\sqrt{3} - \sqrt{5}) (\sqrt{5} + \sqrt{7})$ $(sqrt3 - sqrt5) (sqrt5 + sqrt7)$ ?