Root Calculator — quick guide
1) Core idea
Compute square, cube, and n-th roots, and simplify radicals by pulling perfect powers out of the radical.
2) How this tool works
- n-th Root: finds r with r^n = a (principal root for even n).
- Square/Cube Root: shortcuts for n = 2 and n = 3.
- Simplify Radical: prime-factorizes the radicand and groups n-tuple factors outside.
3) Sanity checks
- a = 0 → root is 0.
- a < 0 with even n → no real root (not supported here).
- a < 0 with odd n → root is negative.
4) Shortcuts that help
- For simplification, group primes in chunks of n; leftovers stay inside.
- Perfect powers come out cleanly: e.g., √(49) = 7, ∛(216) = 6.
- Use factor pairs for quick square roots of small numbers.
5) Common pitfalls
- Assuming √(a + b) = √a + √b (false).
- Forgetting absolute value for even-n roots of a^n.
- Rounding too early—keep exact radicals when possible.
6) Micro-examples
- √72 = 6√2 (pairs: 2×2 and 3×3 come out).
- ∛-8 = -2 (odd root of a negative).
- ⁴√16 = 2 (perfect fourth power).
7) Mini-FAQ
- Decimals? Roots are computed numerically; simplified radicals use integers.
- Complex roots? This tool focuses on real roots.
- Exact vs approx? Simplify radicals for exact form; numeric tabs show decimals.
8) Action tip
When simplifying, prime-factorize first, then extract full n-tuples—don’t mix numeric rounding with symbolic steps.