Question

Rationalize the denominator of 3/6 - √5

Answer 1

multiply numerator and denominator by the conjugate of the denominator
the conjugate of \(a+\sqrt{b}\) is \(a-\sqrt{b}\) and this works because \((a+\sqrt{b})(a-\sqrt{b})=a^2-b\) with no radical
in your case, use \(6+\sqrt{5}\)
\[\frac{3}{6-\sqrt{5}}\times \frac{6+\sqrt{5}}{6+\sqrt{5}}\]
\[=\frac{3(6+\sqrt{5})}{6^2-5}\]
\[=\frac{18+3\sqrt{5}}{36-5}\] etc

Answer 2

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