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How to Put A Cube Root in A Calculator

Reviewed by Calculator Editorial Team

Calculating cube roots is a fundamental mathematical operation that finds the number which, when multiplied by itself three times, equals the original number. This guide explains how to perform cube root calculations using both calculators and manual methods.

How to Calculate a Cube Root

A cube root of a number x is a number y such that y³ = x. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27.

Formula: y = ∛x

Where y is the cube root of x.

Cube roots can be calculated in several ways:

  1. Using a scientific calculator
  2. Using a graphing calculator
  3. Using a computer programming language
  4. Using the long division method manually

Note: Most modern calculators have a dedicated cube root function, but the method for accessing it varies by calculator model.

Calculator Methods

Scientific Calculator

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

  1. Turn on your calculator
  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 see the result

Graphing Calculator

Graphing calculators typically have more advanced functions:

  1. Enter the number in the input field
  2. Use the cube root function (often found in the math menu)
  3. Execute the function to get the result

Online Calculator

Many websites offer online cube root calculators. Simply:

  1. Visit a reliable calculator website
  2. Enter your number in the input field
  3. Click the calculate button
  4. View the result

Manual Calculation Methods

While calculators are convenient, understanding the manual methods can be helpful for learning purposes.

Estimation Method

For simple cube roots, you can estimate:

  1. Find perfect cubes near your number
  2. Interpolate between them to get an approximate answer

Long Division Method

The long division method is more precise:

  1. Divide the number into groups of three digits from right to left
  2. Find the largest number whose cube is less than or equal to the first group
  3. Subtract and bring down the next group
  4. Repeat the process until you've processed all digits

Example: To find ∛125:

  1. 125 is a perfect cube (5³ = 125)
  2. So ∛125 = 5

Common Mistakes

When calculating cube roots, be aware of these common errors:

  • Confusing cube roots with square roots (√x vs ∛x)
  • Using the wrong calculator function (square root instead of cube root)
  • Rounding errors in manual calculations
  • Forgetting to consider negative cube roots (every positive number has one negative cube root)

Tip: Always double-check your calculations, especially when using manual methods.

FAQ

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

A square root finds a number that, when multiplied by itself, equals the original number. A cube root finds a number that, when multiplied by itself three times, equals the original number.

Mathematically: √x = y where y² = x, and ∛x = y where y³ = x.

Can I find the cube root of a negative number?

Yes, every real number has exactly one real cube root. For example, ∛(-8) = -2 because (-2) × (-2) × (-2) = -8.

How accurate are calculator cube root results?

Modern scientific and graphing calculators provide highly accurate results, typically to at least 10 decimal places. Online calculators also offer precise calculations.

Is there a cube root function on all calculators?

Most scientific and graphing calculators have a cube root function. Basic calculators usually don't. If your calculator doesn't have one, you can use the exponent function (yˣ) with x = 1/3.