Simplifying Radicals Practice
An endless supply of never-repeating radical problems with instant feedback. Hunt perfect squares, combine like radicals, multiply, and rationalize — one problem at a time.
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
- Radicals: type
6√2directly, or usesqrt:6sqrt2,6*sqrt(2). Spacing does not matter. - Fractions with radicals:
(5√2)/2or5√2/2— either counts. - Exact form required: a decimal like
8.49is not accepted for6√2— keep the radical. But an unsimplified radical like√72is accepted for6√2.
2 What you’ll practice
Every problem is generated fresh from 12 templates — a problem never repeats until its whole pool is used up.
Simplify
Pull the largest perfect square out of the radicand. Includes perfect squares (which collapse to integers) and bigger hunts.
Combine & multiply
Add and subtract like radicals, simplify-then-add, and multiply radicals (then simplify the product).
Rationalize
Clear radicals from denominators: multiply top and bottom by the radical, then reduce the fraction.
3 Watch out for these
The three mistakes students make most often on radical problems.
Wrong: √9 + √16 = √25 = 5. Right: 3 + 4 = 7 — simplify each first, then combine like radicands.
Wrong: 5√2 → 10. Right: 5√2 stays 5√2 — √2 ≈ 1.414, not 2.
Wrong: 1/√3, done. Right: √3/3 — “no radicals downstairs.”