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How to Take Cubed Root on Calculator

Reviewed by Calculator Editorial Team

Calculating the cubed root is a fundamental math operation that finds the number which, when multiplied by itself three times, gives the original number. This guide explains how to perform cubed root calculations using both calculators and manual methods, with practical examples and common applications.

What is a Cubed Root?

The cubed root of a number x is a value y such that y × y × y = x. In mathematical terms, this is written as y = x^(1/3). For example, the cubed root of 27 is 3 because 3 × 3 × 3 = 27.

Unlike square roots, which have two solutions (positive and negative), cubed roots have only one real solution for real numbers. This makes them particularly useful in volume calculations and other three-dimensional measurements.

Formula: y = x^(1/3)

Where y is the cubed root of x.

How to Calculate Cubed Root

There are two primary methods to calculate the cubed root: using a calculator and manual calculation. Both methods are explained below with examples.

Using a Calculator

Most scientific calculators have a dedicated cubed root function or can calculate it using exponentiation. Here's how to do it:

  1. Enter the number you want to find the cubed root of.
  2. Press the exponentiation key (often labeled as "x^y" or "y^x").
  3. Enter the exponent value of 1/3.
  4. Press the equals (=) key to get the result.

For example, to find the cubed root of 64:

  1. Enter 64.
  2. Press the exponentiation key.
  3. Enter 1/3.
  4. Press equals to get 4.

Note: Some calculators may have a dedicated cubed root function (often labeled as "x³√" or similar). If available, use this for faster results.

Manual Calculation

If you don't have a calculator, you can estimate the cubed root using the following steps:

  1. Find two perfect cubes that the number is between. For example, for 28, the cubes are 27 (3³) and 64 (4³).
  2. Estimate the cubed root by averaging the cube roots of these numbers. For 28, (3 + 4)/2 = 3.5.
  3. Refine your estimate by testing numbers around your initial guess.

For example, to find the cubed root of 28:

  1. Note that 3³ = 27 and 4³ = 64.
  2. Start with 3.5³ = 42.875 (too high).
  3. Try 3.0³ = 27 and 3.1³ = 29.791.
  4. The closest is 3.03³ ≈ 28.00.

This method is less precise than using a calculator but can be useful for quick estimates.

Common Uses of Cubed Root

The cubed root is commonly used in the following scenarios:

  • Volume Calculations: Finding the side length of a cube when given its volume.
  • Engineering: Determining dimensions in three-dimensional designs.
  • Mathematics: Solving equations involving cubic terms.
  • Data Analysis: Calculating geometric means in three dimensions.

For example, if a cube has a volume of 125 cubic units, its side length is the cubed root of 125, which is 5 units.

FAQ

What is the difference between square root and cubed root?
The square root finds a number that, when multiplied by itself twice, equals the original number. The cubed root finds a number that, when multiplied by itself three times, equals the original number.
Can I find the cubed root of a negative number?
Yes, the cubed root of a negative number is also negative. For example, the cubed root of -8 is -2 because (-2) × (-2) × (-2) = -8.
How do I calculate the cubed root of a fraction?
To find the cubed root of a fraction, take the cubed root of the numerator and the denominator separately. For example, the cubed root of 1/8 is 1/2 because (1/2) × (1/2) × (1/2) = 1/8.
What is the cubed root of zero?
The cubed root of zero is zero because 0 × 0 × 0 = 0.