How do you simplify 7 div(5 - sqrt11)7÷(511)?

1 Answer
Oct 21, 2015

7 div (5-sqrt(11)) = (5+sqrt(11))/27÷(511)=5+112

Explanation:

7div(5-sqrt(11)) = 7/(5-sqrt(11))7÷(511)=7511

rationalizing the denominator:
color(white)("XXX")= 7/(5-sqrt(11)) * (5+sqrt(11))/(5+sqrt(11))XXX=75115+115+11

color(white)("XXX")=(7(5+sqrt(11)))/(25-11)XXX=7(5+11)2511

color(white)("XXX")=(7(5+sqrt(11)))/14XXX=7(5+11)14

color(white)("XXX")=(5+sqrt(11))/2XXX=5+112