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#