Pythagorean Theorem Practice
An endless supply of never-repeating right-triangle problems with instant feedback. Find hypotenuses and legs, simplify radicals, spot Pythagorean triples, and solve the word problems where a² + b² = c² earns its keep.
1 Practice
Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss walks you through the full solution.
How to enter answers
- Whole numbers and decimals:
10,8.06— decimals are accepted within ±0.01. - Radical answers: type
sqrt53,√53, or2sqrt10for simplified form — or type a decimal. Both are accepted. - Yes / no questions: just type
yesorno.
2 What you’ll practice
Every problem is generated fresh from 12 templates — a problem never repeats until its whole pool is used up.
Missing sides
Find the hypotenuse (add the squares, then root) or a leg (subtract, then root). c is always the hypotenuse — the longest side.
Exact radical form
When the answer is not a whole number, leave it exact: simplify the radical
(type sqrt53 or 2sqrt10) or give a decimal.
Triples & word problems
Spot Pythagorean triples, test whether a triangle is right, and solve ladder, diagonal, and screen-size problems.
3 Watch out for these
The three mistakes students make most often on Pythagoras problems.
Wrong: legs 6 and 8 → c² = 100, so “c = 100.” Right: c = √100 = 10. The theorem gives you c² — the last step is always the square root.
Wrong: applying it to any triangle with two known sides. Right: right triangles only — look for the right-angle mark first.
Wrong: hypotenuse 13, leg 5 → 5² + 13² = b². Right: 5² + b² = 13² → b = 12. c is always the hypotenuse.