📐 Root Calculator
By Miikka · CalcBrew · Updated
Formula: √8 =
2.828427125
Simplified form
2√2
The root calculator finds the square root, cube root or any nth root of a number and also shows the answer in simplified radical form. It is handy for students and anyone who needs roots that are both accurate and easy to present.
How the calculator works and what it’s for▾
How taking a root works
A square root answers the question: which number, multiplied by itself, gives the value you entered. The square root of 9 is 3 because 3 × 3 = 9. A cube root multiplies a number by itself three times, and an nth root does so n times.
The calculator also simplifies the radical by pulling out the largest perfect square. That is why √8 becomes 2√2, since 8 = 4 × 2 and √4 = 2.
What you enter and what you get
You provide the number whose root you want and choose the degree — square root, cube root or a custom index.
You receive both the exact decimal value and, where possible, the simplified radical form. This is useful when a teacher expects the answer in radical form rather than as a rounded decimal.
Who benefits from a root calculator
It helps with maths homework, exam preparation and situations where you compute distances via the Pythagorean theorem or derive side lengths from an area.
The simplified form matters most in higher-level problems where an exact answer is required.
Good to know
An even-degree root of a negative number has no real value, but an odd-degree root such as a cube root does exist.
Decimal answers are usually rounded, so use the radical form when you need a fully exact value for further calculation.
🔄 Reviewed June 2026
Frequently asked questions
Cite this calculator
CalcBrew. (2026). Root Calculator. https://calcbrew.com/root-calculator“Root Calculator.” CalcBrew, 2026, calcbrew.com/root-calculator.Link to https://calcbrew.com/root-calculator. Results are estimates; cite the underlying formula or data source for academic work.
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