How do you rationalize the denominator $\frac{2 + \sqrt{3}}{5 - \sqrt{3}}$ $(2+sqrt3)/(5-sqrt3)$ ?

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How do you rationalize the denominator $\frac{2 + \sqrt{3}}{5 - \sqrt{3}}$ $(2+sqrt3)/(5-sqrt3)$ ?

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Answer 1 · 2015-04-01T19:18:54

$\frac{2 + \sqrt{3}}{5 - \sqrt{3}} = \frac{(2 + \sqrt{3}) \times (5 + \sqrt{3})}{(5 - \sqrt{3}) \times (5 + \sqrt{3})}$ $(2 + sqrt(3))/(5 - sqrt(3)) = ((2 + sqrt(3))xx(5 + sqrt(3)))/((5 - sqrt(3))xx(5 + sqrt(3))$

$= \frac{10 + 5 \sqrt{3} + 2 \sqrt{3} + {(\sqrt{3})}^{2}}{25 - {(\sqrt{3})}^{2}}$ $= (10 + 5sqrt(3) + 2sqrt(3) + (sqrt(3))^2)/(25 - (sqrt(3))^2)$

$= \frac{10 + 3 + 8 \sqrt{3}}{25 - 3}$ $= (10 + 3 + 8sqrt(3))/(25 - 3)$

$= \frac{13 + 8 \sqrt{3}}{22}$ $= (13 + 8sqrt(3))/(22)$

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