How do I calculate a square root?

√x = x^(1/2). E.g. √25 = 5, because 5² = 25. The square root of a negative number is not real.

What is simplified radical form?

√8 = √(4×2) = 2√2. Factor out perfect squares from under the radical. 2√2 ≈ 2.828.

Can I take the cube root of a negative number?

Yes — for odd degrees, a negative real root exists: ∛(-8) = -2, because (-2)³ = -8.

What is the nth root?

ⁿ√x = x^(1/n). Square root is the 2nd root, cube root is the 3rd root. Fourth root: ⁴√16 = 2.

📐 Root Calculator

Calculate square root, cube root or any nth root. The calculator also shows the simplified radical form, for example √8 = 2√2.

Number

√8

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.