Question

Rationalizing the denominator

Answer 1

\[5 \over \sqrt{5x} \] rationalizes down to \[5\sqrt{x} \] correct? Or is it \[\sqrt{5x} \over x\]?

Answer 2

\[\frac{5}{\sqrt{5x}}\]\[=\frac{5}{\sqrt{5x}}\times1\]\[=\frac{5}{\sqrt{5x}}\times\frac{\sqrt{5x}}{\sqrt{5x}}\]\[=\frac{5\sqrt{5x}}{5x}\]\[=\dfrac{\sqrt{5x}}{x}\]

Answer 3

\[\dfrac{\sqrt{5x}}{x}\]\[=\dfrac{\sqrt{5}\sqrt{x}}{x}\]\[=\frac{\sqrt{5} x^{\frac12}}{x}\]\[=\sqrt 5x^\left({\frac12-1}\right)\]\[=\sqrt 5x^{-1/2}\]\[=\
\frac{\sqrt 5}{\sqrt x}\]\[=\sqrt\frac5x\]