Root Calculator Guide: Square Roots, Cube Roots and Nth Roots

A root calculator helps find square roots, cube roots, and other nth roots. Roots reverse exponentiation: if a number raised to a power equals a given value, a corresponding root can recover the original number.

What is a square root?

The principal square root of a nonnegative number x is the nonnegative number whose square is x. For example, √49 = 7, because 7² = 49. The equation y² = 49 has two solutions, +7 and −7, but the symbol √49 conventionally refers to the principal root, 7.

How to use a root calculator

1. Open the Root Calculator.
2. Enter the number whose root you want to calculate.
3. Choose the root index if the tool supports square, cube, or nth roots.
4. Calculate the result.
5. Check the answer by raising it to the selected power.

Square roots, cube roots and nth roots

Expression	Result	Check
√64	8	8² = 64
∛27	3	3³ = 27
∛−125	−5	(−5)³ = −125
⁴√81	3	3⁴ = 81

How to calculate roots using exponents

For a positive number a, the nth root can be expressed as a^(1/n). For example, 32^(1/5) = 2, because 2⁵ = 32. This relationship is useful when a calculator offers a power function but no dedicated nth-root key.

Perfect squares and approximate roots

A perfect square has an integer square root. For example, 121 is a perfect square because 11² = 121. Many numbers are not perfect squares: √2 ≈ 1.41421. The decimal is an approximation, not an exact replacement for √2.

Negative numbers and roots

An odd root of a negative real number is real: ∛−8 = −2. An even root of a negative number is not real. For example, √−1 is represented by i in the complex number system. Calculator support for complex results varies.

Common mistakes

• Confusing √x with solving the equation y² = x, which may have two real solutions.
• Assuming all roots of negative numbers are undefined.
• Rounding an irrational root too early.
• Entering a root index of zero, which is not valid.

Frequently asked questions

What is the square root of 144?

12.

What is the cube root of 64?

4.

Is √9 equal to ±3?

No. The principal square root √9 is 3. The equation x² = 9 has solutions x = ±3.

Can a root have a decimal answer?

Yes. Many roots are irrational and are shown as decimal approximations.

Use the Root Calculator to check square, cube, and other supported roots.