Root calculator

Enter the root degree and the number. The result appears at once; for a negative number and an even degree the calculator explains why there is no real root.

Load an example

Root degree

2 is the square root, 3 the cube root. A whole number greater than 1.

Number under the root

A negative number is allowed only for an odd degree.

Root: —

Fill in the fields above — the result is computed on this page.

What do these numbers mean?

We compute it from the formula shown below — not from a prediction model and not from draw history.
√144 = 12 denotes the nonnegative principal root. The equation x² = 144 has two solutions: 12 and −12.
Odd-degree roots allow negative input: ³√(−27) = −3.

These are historical data. Each draw is independent of previous draws, so these numbers do not tell us what will be drawn next.

How do I use this page?

Fill in the fields in the form above — the result recomputes at once, with no page reload.
Under the result you will find the interpretation scale, if the calculator has one: it says which range your value fell into.
The formula we use is shown lower on this page — you can check the arithmetic yourself.
To compute the same for another game or variant, change it in the select field — prices and pools update automatically.

Formula

ⁿ√x = x^(1/n)

n is the root degree, x the number under the root. For x < 0 and odd n we take the root of |x| and restore the minus sign.

Theory — what is an nth root?

An nth root of a number x is a value that, raised to the power n, gives back x. The square root of 16 is 4, because 4 squared equals 16, and the cube root of 27 is 3, because 3 cubed gives 27. The calculator computes a root of any degree for the entered number. For a negative number with an even root degree there is no real result, and the calculator states this explicitly.

Frequently asked questions

What is the fourth root of 16?

2, because 2⁴ = 2 · 2 · 2 · 2 = 16.

Can you take the root of a negative number?

Only for an odd degree: ³√(−8) = −2, ⁵√(−32) = −2. An even-degree root of a negative number does not exist among real numbers.

How does a root differ from a fractional power?

It is the same calculation: ⁿ√x = x^(1/n). The power notation is handier in transformations, the root sign when reading the result.

Root calculator

Formula

Frequently asked questions

See also

Ancient Egyptian units converter

Arithmetic Mean

Basic calculator

My saved selections

Notifications after draws