Find any square root. This free square root calculator gives the decimal value and the simplified radical form (like √72 = 6√2), tells you if it’s a perfect square, and handles cube and nth roots too.
Enter a number to find its square root (or cube/nth root). For square roots, the calculator also gives the simplified radical form, like √72 = 6√2.
The square root of a number is the value that, multiplied by itself, gives that number. Negative numbers have no real square root (the calculator notes this).
How the Square Root Calculator Works
This tool finds the nth root of a number — square root by default, but also cube root or any custom root — and shows the decimal value alongside a simplified radical form for square roots. It also flags whether your number is a perfect square and shows its square and cube for reference.
Formula: Root value = Number^(1/n), where n = 2 for the square root (√), n = 3 for the cube root (∛), or any whole number you choose for an nth root. For the square root specifically, the simplified radical form is found by pulling out the largest perfect-square factor: for example, 72 = 36 × 2, so √72 = √36 × √2 = 6√2. A number is a perfect square when its square root is a whole number (e.g. 49 → 7). Negative numbers have no real square root, since no real number multiplied by itself gives a negative result.
- Number — the value you want to find the root of
- Root type — Square √, Cube ∛, or a custom nth root
- n — which root to take, when “nth root” is selected (e.g. n = 4 for a 4th root)
Example Scenarios
| Number | Root Type | Result |
|---|---|---|
| 72 | Square root | ≈8.49 (simplified: 6√2) |
| 49 | Square root | 7 (perfect square) |
| 27 | Cube root | 3 |
| 16 | 4th root (n=4) | 2 |
| 100 | Square root | 10 (perfect square) |
| -9 | Square root | No real square root |
Square Root Calculator FAQ
What does “simplified radical form” mean, like for √72?
It rewrites a root using the largest perfect-square factor you can pull out. For 72, since 72 = 36 × 2 and 36 is a perfect square, √72 simplifies to 6√2, which is the same value written more compactly.How do I find a cube root instead of a square root?
Switch the “Root” toggle from “Square √” to “Cube ∛” before entering your number. The calculator will then compute the cube root and label the result accordingly.Can I calculate something like a 5th root?
Yes. Choose “nth root” from the Root toggle, then enter your desired root in the “n (which root)” field that appears, such as 5, alongside the number.Why is there no result for negative numbers under a square root?
No real number multiplied by itself produces a negative result, so negative inputs under an even root (like square root) have no real answer. The calculator notes this instead of showing a value.How can I tell if a number is a perfect square?
Enter it with “Square √” selected. The calculator’s “Perfect square?” field will confirm whether the square root comes out to a whole number, like 49 → 7.What’s the difference between the square root and squaring a number?
They’re inverse operations. Squaring (n²) multiplies a number by itself, while the square root asks what number, multiplied by itself, gives you the original value. The calculator shows both n² and n³ alongside the root for comparison.Related Calculators
Roots come up constantly in algebra, so if you’re solving quadratics by hand the quadratic formula calculator uses square roots directly in its solution steps. For working with powers instead of roots, the exponent calculator handles the inverse operation, and the full scientific calculator is handy when you need roots as part of a longer expression.