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Ti 83 Calculator Cube Root

Reviewed by Calculator Editorial Team

Calculating cube roots on a TI-83 calculator is straightforward once you know the correct steps. This guide will walk you through the process, explain the formula, and provide practical examples to help you master this essential mathematical operation.

How to Calculate Cube Roots on TI-83

The TI-83 calculator provides a simple way to find cube roots using its built-in functions. Here's a step-by-step guide to performing this calculation:

  1. Turn on your TI-83 calculator and press the 2ND key followed by the CATALOG key to access the function catalog.
  2. Scroll down to find the cube( function and press ENTER to select it.
  3. Enter the number you want to find the cube root of inside the parentheses. For example, to find the cube root of 27, you would type cube(27).
  4. Press ENTER to calculate the result. The calculator will display the cube root of the number you entered.

Tip

If you need to find the cube root of a negative number, you can use the cube( function with a negative input. The result will be negative, following the mathematical rule that the cube root of a negative number is negative.

Using the cube function is the most straightforward method, but you can also calculate cube roots using the ^ (exponent) key if you prefer. To do this, you would enter the number raised to the power of 1/3, such as 27^(1/3).

Cube Root Formula

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

Cube Root Formula

If \( y \) is the cube root of \( x \), then:

\( y = \sqrt[3]{x} \) or \( y^3 = x \)

For example, the cube root of 27 is 3 because \( 3 \times 3 \times 3 = 27 \). Similarly, the cube root of -8 is -2 because \( (-2) \times (-2) \times (-2) = -8 \).

The TI-83 calculator uses this formula internally when you use the cube( function. It calculates the cube root by finding a number that, when raised to the power of 3, equals the input value.

Worked Examples

Let's look at a few examples to see how the cube root calculation works on the TI-83 calculator.

Example 1: Positive Number

Find the cube root of 64.

  1. Press 2ND then CATALOG to access the function catalog.
  2. Scroll to and select cube(.
  3. Type cube(64) and press ENTER.
  4. The calculator displays 4 as the result.

Verification: \( 4 \times 4 \times 4 = 64 \).

Example 2: Negative Number

Find the cube root of -27.

  1. Press 2ND then CATALOG to access the function catalog.
  2. Scroll to and select cube(.
  3. Type cube(-27) and press ENTER.
  4. The calculator displays -3 as the result.

Verification: \( (-3) \times (-3) \times (-3) = -27 \).

Example 3: Decimal Number

Find the cube root of 0.125.

  1. Press 2ND then CATALOG to access the function catalog.
  2. Scroll to and select cube(.
  3. Type cube(0.125) and press ENTER.
  4. The calculator displays 0.5 as the result.

Verification: \( 0.5 \times 0.5 \times 0.5 = 0.125 \).

Frequently Asked Questions

Can I find cube roots on a TI-83 without using the cube function?

Yes, you can use the exponent key (^) to find cube roots by raising the number to the power of 1/3. For example, to find the cube root of 8, you would enter 8^(1/3).

What happens if I try to find the cube root of zero?

The cube root of zero is zero because \( 0 \times 0 \times 0 = 0 \). The TI-83 will display 0 as the result when you calculate cube(0).

Can I find cube roots of complex numbers on a TI-83?

The TI-83 calculator does not support complex numbers directly. It will display an error if you try to find the cube root of a negative number that doesn't have a real cube root.

Is there a difference between the cube function and the exponent method?

No, both methods will give you the same result. The cube function is a shortcut for raising a number to the power of 1/3. The TI-83 uses the same internal calculation for both approaches.