Find the square root or any nth root of a number, instantly
💡 Why This Matters Square roots show up everywhere from geometry homework to real-world measurements — figuring out a side length from an area, checking standard deviation, or just settling a math debate. This tool gives you the exact answer and, for nth roots, lets you go beyond just square and cube.
The radical symbol (√) has been used for roots since the 1500s — it likely evolved from a stylized lowercase "r," short for the Latin word "radix," meaning root.
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The square root of a number x is the value that, when multiplied by itself, equals x. This calculator generalizes that to any root: for a root of degree n, it finds the value that, raised to the nth power, equals your input. Mathematically, that's x^(1/n) — the calculator uses this exponent form under the hood so it works for square roots, cube roots, and beyond, not just perfect squares.
If your number is a perfect square (like 16, 25, or 81), the result will be a clean whole number. Most numbers aren't perfect squares, though — in that case you'll get a decimal, which is the honest, exact-enough answer rather than an approximation to round away. For odd-degree roots (cube root, 5th root, etc.), negative inputs are also solvable — for even-degree roots like square root, negative inputs have no real-number answer.
This calculator works in real numbers only — it won't return imaginary results for negative numbers under an even root (like √-9). Very large numbers or very high root degrees may show results in scientific notation depending on your browser, and rounding is applied for display, so extremely precise scientific or engineering work should double-check with dedicated software.
Use the result directly in geometry (finding a side length from an area), statistics (standard deviation is a square root by definition), physics, or everyday problem-solving. Try a few perfect squares first (4, 9, 16, 25) to get a feel for how the tool behaves before running your real numbers.
Example: Say you want the square root of 50. It's not a perfect square, but 50 = 25 × 2, and 25 is a perfect square. So √50 = √25 × √2 = 5 × √2 ≈ 5 × 1.41421 = 7.071. Plugging 50 into this calculator with root degree 2 gives you that same 7.071 directly.
A perfect square is a number that's the result of multiplying an integer by itself — like 4 (2×2), 25 (5×5), or 144 (12×12). Its square root is always a whole number.
Not with real numbers — no real number multiplied by itself gives a negative result. Negative inputs require imaginary numbers (using i, where i² = -1), which this calculator doesn't compute.
A square root asks "what number times itself equals this?" A cube root asks the same question but for a number multiplied by itself three times. Cube roots can handle negative numbers; square roots (in real numbers) can't.
Break the number into its largest perfect-square factor and pull that factor out. For example, √50 = √(25 × 2) = 5√2, since 25 is a perfect square hiding inside 50.