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How to Take A Cube Root on A Graphing Calculator

Reviewed by Calculator Editorial Team

Calculating cube roots is a fundamental math operation with applications in geometry, algebra, and real-world measurements. This guide explains how to find cube roots using a graphing calculator, including step-by-step instructions, formulas, and practical examples.

What is a Cube Root?

The cube root of a number x is a value y such that y³ = x. In other words, it's the number that, when multiplied by itself three times, gives the original number. 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 are defined for all real numbers, but they can be irrational for some values. For example, ∛2 ≈ 1.2599, which is an irrational number.

Using a Graphing Calculator

Most modern graphing calculators can compute cube roots directly. Here's how to do it on common models:

TI-84 Series

  1. Press the MATH button
  2. Use the arrow keys to select Math and then 3: cube(
  3. Enter the number you want to find the cube root of inside the parentheses
  4. Press ENTER to see the result

Casio fx-CG50

  1. Press the MENU button
  2. Select Math and then Cube Root
  3. Enter the number
  4. Press EXE to calculate

HP Prime

  1. Enter the number
  2. Press the ^ button (power)
  3. Enter 1/3
  4. Press ENTER to see the result

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

Manual Calculation Method

If you need to calculate a cube root without a calculator, you can use the following approximation method:

Step-by-Step Approximation

  1. Start with an initial guess. For example, to find ∛10, you might start with 2 because 2³ = 8 and 3³ = 27.
  2. Divide the original number by the cube of your guess: 10 ÷ (2³) = 10 ÷ 8 = 1.25
  3. Add 1 to this result: 1.25 + 1 = 2.25
  4. Divide by 3: 2.25 ÷ 3 ≈ 0.75
  5. Add this to your original guess: 2 + 0.75 = 2.75
  6. Repeat the process with your new guess until you reach a satisfactory level of precision.

Approximation Formula:

y ≈ (x/(y₀³) + 1)/3 + y₀

Where y₀ is the initial guess and y is the improved approximation.

This method typically converges to the correct cube root within 3-5 iterations for most numbers.

Common Mistakes to Avoid

  • Confusing cube roots with square roots - remember, cube roots are the third root, not the second.
  • Forgetting that cube roots can be negative - for example, ∛(-8) = -2.
  • Using the wrong exponent when calculating manually - always use 1/3 for cube roots.
  • Rounding too early in manual calculations - keep more decimal places until the final answer.

Tip: Always verify your cube root calculations by cubing the result to ensure it matches the original number.

FAQ

Can I find cube roots of negative numbers?

Yes, cube roots of negative numbers are defined and will also be negative. For example, ∛(-27) = -3 because (-3) × (-3) × (-3) = -27.

What's the difference between a cube root and a square root?

The cube root finds a number that, when multiplied by itself three times, gives the original number. The square root finds a number that, when multiplied by itself twice, gives the original number. For example, √9 = 3 and ∛27 = 3.

How do I calculate cube roots of fractions?

You can calculate cube roots of fractions by treating them as decimals. For example, ∛(1/8) = 0.5 because 0.5 × 0.5 × 0.5 = 0.125 = 1/8.

What's the cube root of 1?

The cube root of 1 is 1 because 1 × 1 × 1 = 1.