Rationalising a one-term denominator

Rationalising replaces a surd denominator with a rational denominator without changing the value. Multiply numerator and denominator by the same nonzero surd.

Example

\(\dfrac5{\sqrt3}=\dfrac{5\sqrt3}{3}\). Also \(\dfrac6{2\sqrt5}=\dfrac3{\sqrt5}=\dfrac{3\sqrt5}{5}\).

With a numerator containing a sum, multiply every term: \(\dfrac{2+\sqrt3}{\sqrt3}=\dfrac{2\sqrt3+3}{3}\).

The denominator here is a single surd term. Check the result by multiplying it by the original denominator; it must recover the original numerator.