Roots undo powers: √144 asks "what, squared, gives 144?" (answer: 12). This calculator handles any root and any integer power — and for square roots of whole numbers it also produces the exact simplified radical your math teacher wants.
Simplifying radicals
√48 isn't "wrong" as 6.9282…, but the exact form carries more truth: 48 = 16 × 3, so √48 = 4√3. The calculator hunts the largest perfect-square factor automatically — √72 → 6√2, √200 → 10√2 — and says "= n exactly" when the number is a perfect square.
Negative numbers: the even/odd split
Odd roots of negatives are perfectly real — ∛−8 = −2, since (−2)³ = −8. Even roots are not: no real number squares to −9, and the calculator says so plainly, noting the complex-plane answer (3i) rather than erroring. That even/odd asymmetry is the whole story of why the quadratic formula sometimes "has no real solutions" — see it in action in the quadratic calculator.
Roots are just fractional exponents
x^(1/2) is √x — same object, different clothes. That identity makes the exponent laws do all the work: x^(3/2) is "square root, then cube," and ⁿ√(xᵐ) = x^(m/n). The "as exponent" badge keeps the translation visible.
How machines actually take roots
Heron of Alexandria's 2,000-year-old method still wins: guess g, replace it with the average of g and x/g, repeat. Each pass doubles the correct digits — √2 from a guess of 1 reaches 1.41421 in four steps. Modern CPUs refine the same idea in silicon.
Results to double precision; radical simplification for integer square roots.