Square Root and N-th Root Calculator
Calculate the square root, cube root or n-th root. For negative numbers, use an odd index.
Tip: √ is the square root (n=2), ∛ the cube root (n=3). You can calculate any n-th root.
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About this digital tool
The root calculator finds the square root, cube root or any n-th root of a number. Enter the number and the index n (2 for square, 3 for cube) and get the result instantly, together with the starting value and the degree.
The n-th root of a is the number that, raised to the power n, gives a. For example, √144 = 12 because 12² = 144, ∛27 = 3 because 3³ = 27 and the 5th root of 32 is 2 because 2⁵ = 32. An even root of a negative number is not real, while an odd root is allowed: ∛(−8) = −2. It is used in geometry, in physics, in finance (growth rate) and in algebra.
How to use
- Enter the number you want to take the root of.
- Choose the index n: 2 for square root, 3 for cube root, or another value.
- Read the result in the result bar.
- For negative numbers use only an odd index, otherwise there is no real result.
Frequently asked questions
Does a negative number have a square root?
Not in the real numbers. For example, √(−1) = i is an imaginary number and is not calculated by this tool.
Can I calculate the cube root of a negative number?
Yes. An odd index allows real roots of negative numbers; for example, ∛(−8) = −2.
How do I calculate the cube root of a number?
Set the index n = 3. The cube root is the number that multiplied by itself three times gives the original number. E.g. ∛64 = 4 because 4 × 4 × 4 = 64.
What is the square root of 2?
About 1.41421, an irrational number that never ends. Check: 1.41421² ≈ 2.