How do you simplify #(sqrt(3) - 2) / (-5*sqrt(3)+8)#?

1 Answer
Jun 12, 2017

Answer:

#color(green)((1+2sqrt3)/11#

Explanation:

#(sqrt3-2)/(-5*sqrt3+8)#

#(sqrt3-2)/(-5*sqrt3+8) xx (-5sqrt3-8)/(-5sqrt3-8)# (conjugate)

#color(white)(aaaaaaaaaaaaa)##sqrt3-2#
#color(white)(aaaaaaaa)## xx underline(-5sqrt3-8)#
#color(white)(aaaaaaaaaaaaa)##(-5*3)+10sqrt3#
#color(white)(aaaaaaaaaaaaaaaaaaaaaa)##-8sqrt3+16#
#color(white)(aaaaaaaaaaaaaaaaaa)##overline(-15+2sqrt3+16)#

#color(white)(aaaaaaaaaaaaa)##color(green)(1+2sqrt3# numerator

#color(white)(aaaaaaaaaaaaa)##-5sqrt3+8#
#color(white)(aaaaaaaaaaa)## xx underline(-5sqrt3-8)#
#color(white)(aaaaaaaaaaaaa)##(25*3)-40sqrt3#
#color(white)(aaaaaaaaaaaaaaaaaaaa)##ul(+40sqrt3-64)#
#color(white)(aaaaaaaaaaaaaaaaaa)##75-64#

#color(white)(aaaaaaaaaaaaa)##color(green)(11# denominator

#:.color(green)(=(1+2sqrt3)/11#

Check:

#color(red)((sqrt3-2)/(-5*sqrt3+8)=0.405827418#

#color(red)((1+2sqrt3)/11=0.405827418#