#25
Top 50 Mistake
Forgetting to square root or doing it incorrectly H
"The Root of the Problem"
The Mistake in Action
Make $r$ the subject of $A = \pi r^2$
Wrong: $\frac{A}{\pi} = r^2$ $r = \frac{A}{\pi} - 2$
Why It Happens
Students see $r^2$ and subtract 2 instead of taking the square root. They confuse the exponent with a term being added.
The Fix
The inverse of squaring is taking the square root, not subtracting 2.
$$A = \pi r^2$$
Divide by $\pi$: $$\frac{A}{\pi} = r^2$$
Take the square root: $$r = \sqrt{\frac{A}{\pi}}$$
Note: For GCSE, we typically only consider the positive root for measurements like radius.
Spot the Mistake
Can you identify where this student went wrong?
Make $r$ the subject of $A = \pi r^2$
$\frac{A}{\pi} = r^2$
$r = \frac{A}{\pi} - 2$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: