How do you simplify sqrt6+2sqrt66+26?

1 Answer
Sep 4, 2015

=color(blue)(-18=18

Explanation:

sqrt6+2sqrt66+26 can be simplified by multiplying the expression by its conjugate term which is =color(blue)(sqrt6-2sqrt6=626

=(sqrt6+2sqrt6) * (color(blue)(sqrt6-2sqrt6))=(6+26)(626) , here we can apply the below property:
(a+b)(a-b) = color(blue)((a^2-b^2)(a+b)(ab)=(a2b2)

=(sqrt6+2sqrt6) * (color(blue)(sqrt6-2sqrt6)) = (sqrt6)^2-(2sqrt6)^2=(6+26)(626)=(6)2(26)2

=6 -24=624
=color(blue)(-18=18