Root Calculator
Calculate nth roots and square roots
Root Calculator tool
Result
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Radical Form:
Decimal:
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Step-by-step:
- 1.Number: 64
- 2.Root degree: 3 (cube root)
- 3.Calculate: 64^(1/3)
- 4.Result: 0
Root Calculator: key facts
- What it does
- Calculate nth roots and square roots
- Category
- Math Calculators
- Cost
- Free, with no account, sign-up, or install.
- Your data
- Runs entirely in your browser — the files and text you enter are never uploaded to a server.
- Last reviewed
- . Report an incorrect result.
Understanding the Root Calculator
Square roots, cube roots, and higher roots all answer the same question: what number, multiplied by itself a certain number of times, gives this value? This calculator finds any root you ask for — enter a number and a root degree, and it returns the result as a decimal and in radical notation.
Students checking algebra and geometry work use it constantly, as do people working with formulas involving areas, volumes, or growth rates. Quick buttons cover the square, cube, and fourth roots for the most common cases, while the degree field handles any nth root you need.
Getting a result
- Enter the number you want the root of.
- Enter the root degree (2 for square root, 3 for cube root, and so on) — or tap a quick-root button.
- Read the decimal result.
- Check the radical-notation form and the step-by-step breakdown.
Any degree of root, via fractional powers
Rather than implementing separate square and cube root routines, the tool raises the number to the reciprocal of the root degree. The nth root is the one-nth power, so a single exponentiation handles every degree — square, cube, fourth, or anything else you enter.
A root asks the inverse question to a power: not what you get by multiplying a number by itself repeatedly, but what number would have to be multiplied that way to arrive here. The tool also renders the radical form so the notation matches how the expression would be written by hand.
Results are frequently irrational, meaning no finite decimal represents them exactly. The square root of two is the classic case, and what you see displayed is a truncation rather than the value itself.
- The defaults — the cube root of 64 — give exactly 4, since 4 × 4 × 4 = 64.
- The square root of 2 is 1.4142 to four places, and continues without repeating forever.
- The fourth root of 81 is 3, because 3 to the fourth power is 81.
Reasons to use it here
- It computes any nth root, not just square roots, so cube and higher roots are one entry away.
- Quick buttons for the square, cube, and fourth roots cover the everyday cases without typing a degree.
- It displays the answer in proper radical notation alongside the decimal, reinforcing the math.
- Calculations happen instantly on your device with no sign-up.
Negative numbers, and the two square roots
Odd-degree roots of negative numbers exist among the reals — the cube root of −8 is −2, because an odd number of negative factors stays negative. Even-degree roots of negatives do not, since any real number raised to an even power is positive. Those cases require imaginary numbers, and this calculator works in the reals only.
Every positive number technically has two square roots, one positive and one negative, because both squared give the same result. By convention the radical symbol denotes the principal, non-negative root, which is what is returned here. That convention is why solving an equation by taking a square root requires the plus-or-minus explicitly — forgetting it loses half the solutions.
Where roots come up in practice is usually geometry and statistics. Recovering a side length from an area needs a square root, an edge from a volume needs a cube root, and standard deviation is a square root applied to variance to bring the figure back into the units of the original data.
Frequently Asked Questions
What does the root degree mean?
The degree is how many times the result is multiplied by itself to get your number. A degree of 2 is a square root, 3 is a cube root, 4 is a fourth root, and so on. This calculator accepts any degree you enter.
Can I take the root of a negative number?
Odd roots of negatives are real — the cube root of −8 is −2, for instance. Even roots of negative numbers, like the square root of −4, are not real numbers, so those will not return a valid decimal result here.
What is radical form?
Radical form writes the operation with the root symbol, such as √64 or ³√27, rather than as a decimal. The calculator shows both so you can present the answer either way, which is handy for schoolwork.
How is a root related to an exponent?
Taking the nth root is the same as raising to the power of 1/n — a square root is the power 0.5, a cube root is the power one-third. That is exactly how this calculator computes roots, which is why it handles any degree you enter.
