How do you rationalize the denominator and simplify $((sqrt7) - (sqrt 2))/((sqrt7) + (sqrt 2))$ ?

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Answer 1 · 2016-04-29T16:22:29

$(9-2sqrt(14))/5$

Given: $" "color(brown)((sqrt(7)-sqrt(2))/(sqrt(7)+sqrt(2)))$

Trick is to use the scenario: $" "a^2-b^2=(a+b)(a-b)$

Multiply by 1 but in the form $color(blue)(1=(sqrt(7)-sqrt(2))/(sqrt(7)-sqrt(2)))$

$color(brown)((sqrt(7)-sqrt(2))/(sqrt(7)+sqrt(2)))color(blue)( xx (sqrt(7)-sqrt(2))/(sqrt(7)-sqrt(2)))$

$(sqrt(7)-sqrt(2))^2/((sqrt(7))^2-(sqrt(2))^2)$

$(7-2sqrt(7)sqrt(2)+2)/(7-2)$

$(9-2sqrt(14))/5$

How do you rationalize the denominator and simplify ((sqrt7) - (sqrt 2))/((sqrt7) + (sqrt 2)) ((sqrt7) - (sqrt 2))/((sqrt7) + (sqrt 2))?