Root of 3rd on Calculator

Calculating the cube root of a number is a fundamental mathematical operation that finds the value which, when multiplied by itself three times, gives the original number. This guide explains how to find the root of 3rd degree using our calculator, understand the formula, and interpret results.

What is a cube root?

The cube root of a number x is a value y such that y × y × y = x. In mathematical terms, it's the inverse operation of cubing a number. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27.

Cube roots are important in geometry for finding edge lengths of cubes, in algebra for solving cubic equations, and in various scientific calculations. They can be positive or negative depending on the original number's sign.

How to calculate cube roots

There are several methods to find cube roots:

Using our calculator (recommended for most users)
Using the cube root function on scientific calculators
Using logarithms (advanced method)
Estimation and trial (for simple cases)

The calculator method is the most straightforward for most users, especially when dealing with complex numbers or precise calculations.

Cube root formula

The cube root of a number x can be expressed as:

∛x = y, where y × y × y = x

For real numbers, the cube root is defined for all real numbers, with the result being negative when x is negative. For complex numbers, cube roots can have three distinct values.

Worked examples

Example 1: Positive integer

Find the cube root of 64.

Solution: We know that 4 × 4 × 4 = 64, so ∛64 = 4.

Example 2: Negative number

Find the cube root of -27.

Solution: We know that -3 × -3 × -3 = -27, so ∛(-27) = -3.

Example 3: Decimal number

Find the cube root of 0.125.

Solution: We know that 0.5 × 0.5 × 0.5 = 0.125, so ∛0.125 = 0.5.

Note: For non-perfect cubes, the calculator will provide an approximate decimal value.

FAQ

What is the difference between square root and cube root?: The square root finds a number that, when multiplied by itself, gives the original number (√x = y where y × y = x). The cube root finds a number that, when multiplied by itself three times, gives the original number (∛x = y where y × y × y = x).
Can I find the cube root of a negative number?: Yes, the cube root of a negative number is negative. For example, ∛(-8) = -2 because -2 × -2 × -2 = -8.
What is the cube root of 1?: The cube root of 1 is 1 because 1 × 1 × 1 = 1.
How accurate is the calculator's cube root function?: The calculator uses JavaScript's built-in Math.cbrt() function which provides precise results for all real numbers.
Can I use this calculator for complex numbers?: This calculator currently handles real numbers only. For complex cube roots, you would need specialized mathematical software.