How do you simplify -6/(5-sqrt11)?

1 Answer
Mar 22, 2017

-(30 + 6sqrt(11))/36

Explanation:

rationalise the denominator.

use this law:
(a+b)(a-b) = a^2 - b^2

to rationalise 5-sqrt(11), multiply it by 5+sqrt(11):

5+sqrt(11)*5-sqrt(11) = 5^2 + (sqrt(11))^2

=25+11

=36

multiply the numerator by 5+sqrt(11) as well:

6*(5+ sqrt(11)) = 30 + 6sqrt(11)

fraction: -(30 + 6sqrt(11))/36