Cal11 calculator
Search calculator...

How to Remove A Cube Root Using Calculator

Reviewed by Calculator Editorial Team

Removing a cube root means finding the number that, when multiplied by itself three times, gives the original number. This is the inverse operation of cubing a number. Calculators make this process quick and accurate, but understanding the underlying math helps you use them effectively.

What is a cube root?

The cube root of a number x is a number y such that y × y × y = x. In mathematical terms, this is written as y = ∛x. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27.

Cube roots are important in many areas of mathematics, including algebra, geometry, and calculus. They appear in problems involving volumes, where the side length of a cube is related to its volume by the cube root function.

How to remove a cube root

Removing a cube root can be done using either a calculator or manual methods. Both approaches involve understanding the relationship between the original number and its cube root.

Formula

To remove a cube root, you need to find the number y such that y³ = x. This is the inverse operation of cubing a number.

Using a calculator

Modern scientific calculators have a built-in cube root function, making this calculation quick and easy. Here's how to use a calculator to remove a cube root:

  1. Enter the number you want to find the cube root of.
  2. Press the cube root button (often labeled as ∛ or with a similar symbol).
  3. Press the equals (=) button to get the result.

For example, to find the cube root of 64:

  1. Enter 64 on your calculator.
  2. Press the ∛ button.
  3. Press = to get 4, since 4 × 4 × 4 = 64.

Tip

If your calculator doesn't have a dedicated cube root button, you can use the exponent function (yˣ) by entering the number and raising it to the power of 1/3.

Manual calculation

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

  1. Find two perfect cubes between which your number lies.
  2. Estimate the cube root by averaging the cube roots of these perfect cubes.
  3. Refine your estimate using trial and error.

For example, to find the cube root of 20:

  1. Note that 27 (3³) is greater than 20, and 8 (2³) is less than 20.
  2. Estimate the cube root as between 2 and 3.
  3. Try 2.5: 2.5 × 2.5 × 2.5 = 15.625 (too low).
  4. Try 2.7: 2.7 × 2.7 × 2.7 ≈ 19.683 (close to 20).
  5. Adjust further to get a more precise estimate.

Common mistakes

When removing cube roots, several common mistakes can occur:

  • Confusing cube roots with square roots: Remember that cube roots involve multiplying a number by itself three times, not two.
  • Using the wrong exponent: Cube roots are the inverse of cubing, so raising to the power of 1/3 is correct, not 1/2.
  • Rounding errors: When estimating manually, be careful not to round too early, as this can lead to inaccurate results.

FAQ

What is the difference between a square root and a cube root?

A square root is the number that, when multiplied by itself, gives the original number. A cube root is the number that, when multiplied by itself three times, gives the original number.

Can I use a calculator to find cube roots of negative numbers?

Yes, most scientific calculators can handle negative numbers for cube roots. The result will also be negative, following the rule that the cube root of a negative number is negative.

How do I find the cube root of a fraction?

To find the cube root of a fraction, you can separate the numerator and denominator and find their cube roots individually. For example, ∛(8/27) = ∛8 / ∛27 = 2/3.