How do you rationalize the denominator and simplify $\frac{2 + \sqrt{11}}{5 - \sqrt{11}}$ $(2+sqrt11)/(5-sqrt11)$ ?

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Answer 1 · 2015-04-12T18:02:45

To rationalize a denominator:
Multiply the numerator and denominator by the conjugate of the denominator.

$\frac{2 + \sqrt{11}}{5 - \sqrt{11}} \times \frac{5 + \sqrt{11}}{5 + \sqrt{11}}$ $(2+sqrt(11))/(5-sqrt(11))xx(5+sqrt(11))/(5+sqrt(11))$

$= \frac{10 + 7 \sqrt{11} + 11}{25 - 11}$ $=(10 +7sqrt(11)+11)/(25-11)$

$= \frac{21 + 7 \sqrt{11}}{14}$ $= (21+7sqrt(11))/(14)$

$= \frac{3 + \sqrt{11}}{2}$ $= (3+sqrt(11))/2$

How do you rationalize the denominator and simplify 2+√115−√11(2+sqrt11)/(5-sqrt11)?