Leaving a surd in the denominator H
"The Forgotten Rationalise"
The Mistake in Action
Write $\frac{6}{\sqrt{3}}$ in the form $a\sqrt{3}$
Wrong: $\frac{6}{\sqrt{3}}$ is already simplified — it can't be written in that form.
Why It Happens
Students don't recognise that rationalising the denominator will give the required form.
The Fix
Rationalise by multiplying by $\frac{\sqrt{3}}{\sqrt{3}}$:
$$\frac{6}{\sqrt{3}} = \frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{6\sqrt{3}}{3} = 2\sqrt{3}$$
So $a = 2$.
Key insight: Rationalising doesn't just "tidy up" — it often transforms expressions into new forms.
Spot the Mistake
Can you identify where this student went wrong?
$\frac{6}{\sqrt{3}}$ cannot be written in the form $a\sqrt{3}$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: