Root Calculator
Find the square root, cube root or any nth root of a number — free and instant. Get the exact simplified radical form as well as the decimal value, all computed privately in your browser.
How to use the Root Calculator
- Pick the root type. Choose a square root, a cube root, or the nth-root option to enter your own degree (4th root, 5th root, and so on).
- Enter your number. Type the value under the radical — the radicand. It can be a whole number or a decimal, and negative numbers work for odd roots such as cube roots.
- Read the answer. The decimal value appears instantly, along with the simplified radical form (for example √72 = 6√2), the scientific notation and the equivalent exponent form.
About this tool
This free root calculator finds the principal nth root of any number, written mathematically as x^(1/n) or as a radical ⁿ√x. Enter 2 for a square root, 3 for a cube root, or any whole degree for higher roots. Beyond the decimal value it also simplifies the radical to its exact lowest form by pulling out perfect nth-power factors, so √72 becomes 6√2 and ∛54 becomes 3·∛2 — the kind of exact answer that homework and algebra classes ask for. When the number is a perfect square, cube or nth power, the calculator reports the exact whole-number root.
Everything is computed locally in your browser, so nothing you type is uploaded or stored. Remember that even roots (square, 4th, 6th…) of a positive number have two real values, plus and minus, and that even roots of a negative number are not real numbers. Odd roots such as cube roots keep the sign of the original number. For the opposite operation of raising a number to a power, use the Exponent Calculator, and to find an unknown power try the Logarithm Calculator.
Frequently asked questions
How does simplifying a radical work?
The calculator factors the number under the root and pulls out every group that forms a perfect nth power. For a square root, √72 = √(36 × 2) = 6√2, because 36 is the largest perfect square that divides 72. The leftover factor stays inside the radical. Simplified radical form is available for whole-number radicands.
Can I take the root of a negative number?
Only for odd roots. The cube root of −8 is −2, and any odd root keeps the negative sign. Even roots — square roots, 4th roots, 6th roots and so on — of a negative number have no real value; the answer would be a complex number, so the tool shows a clear message instead.
Why does a square root have two answers?
Because both +r and −r, when squared, give the same positive number: 5² and (−5)² are both 25, so the two square roots of 25 are +5 and −5. Calculators report the principal (non-negative) root by default, which is the +5 shown here, and the note reminds you of the negative solution.
What is the difference between a root and a fractional exponent?
They are the same thing. The nth root of x equals x raised to the power 1/n, so ∛8 is identical to 8^(1/3) = 2. The calculator shows this exponent form as one of its results so you can move between the two notations easily.