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

1 Answer
Apr 29, 2016

Answer:

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

Explanation:

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#