Finding $c^2$ instead of $c$
"The Forgotten Root"
The Mistake in Action
Find the hypotenuse of a right-angled triangle with sides 5cm and 12cm.
Wrong: $c^2 = 5^2 + 12^2 = 169$ $c = 169$ cm
Why It Happens
Students correctly apply the formula and find $c^2$, but forget the final step: taking the square root.
The Fix
The formula gives you $c^2$, not $c$. You must take the square root at the end!
$$c^2 = 5^2 + 12^2 = 25 + 144 = 169$$ $$c = \sqrt{169} = 13\text{cm}$$
Tip: Always ask yourself: "Is my answer sensible?" 169cm is much longer than either side ā the hypotenuse should be longer but not ridiculously so!
Spot the Mistake
Can you identify where this student went wrong?
Find the hypotenuse. Shorter sides are 5cm and 12cm.
$c^2 = 5^2 + 12^2 = 25 + 144 = 169$
$c = 169$ cm
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: