Question

Simplify the expression leaving in surd form if appropriate

Answer 1

\[\frac{ 7-\sqrt{11} }{4+\sqrt{11} }\]

Answer 2

multiply both numeartor and denominator with 4-sqrt11)

Answer 3

Usual tactic when you have something like this is to multiply both top and bottom by the conjugate of the denominator. Here that would mean multiplying by \[\frac{4-\sqrt{11}}{4-\sqrt{11}}\]

Answer 4

You get a difference of squares which clears up the square root in the denominator. Also works for trig, complex numbers, etc.

Answer 5

(7-sqrt(11)) (4-sqrt(11))/ ((4+sqrt(11)) *(4-sqrt(11))
=(28- 4sqrt(11) - 7 sqrt(11) +11)/ (16 -11)
=(39 -11sqrt(11) )/5

Answer 6

Ok that makes sense, thanks for the help guys