Simplify the expression by rationalizing the denominator. State results in exact form.

Question

Quizplus · Accepted Answer

We need to rationalize the denominator, which means we need to eliminate the radical from it. To do this, we can multiply the numerator and denominator by the conjugate of the denominator, which is (5-2√2):

$\frac{11}{5+\sqrt{18}} \cdot \frac{5-\sqrt{18}}{5-\sqrt{18}} = \frac{11(5-\sqrt{18})}{25-18} = \frac{11(5-\sqrt{18})}{7}$

This is the simplified expression in exact form. The corresponding choice is (C).

Simplify the Expression by Rationalizing the Denominator