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How to Take The Cube Root on Calculator

Reviewed by Calculator Editorial Team

Calculating cube roots is a fundamental mathematical operation that finds applications in geometry, algebra, and real-world measurements. This guide explains how to find cube roots using both calculators and manual methods, along with practical examples and common pitfalls to avoid.

How to Calculate Cube Roots

The cube root of a number x is a value that, when multiplied by itself three times, gives the original number. Mathematically, this is represented as:

Cube Root Formula

If y = ∛x, then y × y × y = x

For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27. Cube roots can be positive or negative depending on the original number. For instance, ∛(-8) = -2 because (-2) × (-2) × (-2) = -8.

Using a Calculator

Most scientific calculators have a dedicated cube root function. Here's how to use it:

  1. Turn on your calculator and clear any previous calculations.
  2. Enter the number you want to find the cube root of.
  3. Press the cube root button (often labeled as "x³" or "³√x").
  4. Press the equals (=) button to display the result.

Note

If your calculator doesn't have a cube root button, you can calculate it by raising the number to the power of 1/3 (x^(1/3)).

Manual Calculation Methods

Estimation Method

For numbers without perfect cube roots, you can estimate:

  1. Find perfect cubes near your number.
  2. Interpolate between these values.
  3. Refine your estimate using trial and error.

Long Division Method

This method is more precise but requires more steps:

  1. Group digits in pairs from the decimal point to the right.
  2. Find the largest number whose cube is less than the first group.
  3. Subtract and bring down the next pair.
  4. Repeat the process to find the cube root digit by digit.

Common Mistakes

  • Assuming all numbers have perfect cube roots - only perfect cubes (like 8, 27, 64) have exact integer cube roots.
  • Forgetting that cube roots can be negative - the cube root of a negative number is negative.
  • Using the square root button instead of the cube root function.
  • Rounding too early in manual calculations, which can lead to significant errors.

Real-World Examples

Cube roots appear in various practical applications:

Scenario Calculation Result
Volume of a cube with side length 5 cm 5 × 5 × 5 = 125 cm³ Cube root of 125 is 5 cm
Finding the edge length of a cube with volume 216 in³ ∛216 ≈ 6 in Each edge is approximately 6 inches

FAQ

Can I find cube roots of negative numbers?

Yes, the cube root of a negative number is negative. For example, ∛(-27) = -3 because (-3) × (-3) × (-3) = -27.

What if my calculator doesn't have a cube root button?

You can calculate the cube root by raising the number to the power of 1/3 (x^(1/3)).

How do I know if a number is a perfect cube?

A number is a perfect cube if it can be expressed as n³ where n is an integer. Examples include 1, 8, 27, 64, etc.