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How to Input Cube Root Into A Ti 83 Calculator

Reviewed by Calculator Editorial Team

The TI-83 calculator is a powerful tool for mathematical calculations, including cube roots. This guide will walk you through the process of inputting cube root calculations on your TI-83, covering basic operations, negative numbers, decimal results, and common mistakes to avoid.

Basic Cube Root Calculation

To find the cube root of a number on your TI-83 calculator, follow these steps:

  1. Press the 2ND key and then the √x key to access the cube root function (it will display as x√).
  2. Enter the number you want to find the cube root of. For example, to find the cube root of 27, press 2, 7.
  3. Press the = key to calculate the result. The TI-83 will display 3 as the cube root of 27.

Tip: Remember that the cube root of a number x is a value that, when multiplied by itself three times, gives x. In mathematical terms: y = x^(1/3).

Cube Root of Negative Numbers

The TI-83 can also calculate cube roots of negative numbers:

  1. Press 2ND then √x to access the cube root function.
  2. Enter the negative number. For example, to find the cube root of -8, press -, 8.
  3. Press =. The calculator will display -2 as the result.

Formula: The cube root of a negative number is negative. For example, ∛(-8) = -2 because -2 × -2 × -2 = -8.

Decimal Results

When dealing with numbers that don't have perfect cube roots, the TI-83 will display decimal approximations:

  1. Press 2ND then √x.
  2. Enter a number without a perfect cube root, such as 10.
  3. Press =. The calculator will display approximately 2.15443469.

This decimal approximation is accurate to 9 decimal places, which is sufficient for most practical purposes.

Common Mistakes

Avoid these common errors when working with cube roots on your TI-83:

  • Confusing square roots with cube roots: Remember that the square root function is accessed with the √x key, while cube roots require pressing 2ND first.
  • Forgetting to press 2ND: Always press the 2ND key before the √x key to access the cube root function.
  • Entering numbers incorrectly: Double-check your number entry to ensure accuracy.

Advanced Usage

You can combine cube roots with other operations on your TI-83:

  1. Calculate the cube root of a sum: 2ND √x ( 5 + 3 ) = will display 2.08008382.
  2. Find the cube root of a product: 2ND √x ( 2 × 4 ) = will display 2.5198421.
  3. Calculate the cube root of a fraction: 2ND √x ( 8 ÷ 2 ) = will display 1.58740105.

These advanced operations follow the same principles as basic cube root calculations but involve additional mathematical operations.

Frequently Asked Questions

Can I find the cube root of a negative number on a TI-83?

Yes, the TI-83 can calculate cube roots of negative numbers. The result will be negative, as shown in the example for -8.

How accurate are the decimal results on the TI-83?

The TI-83 provides cube root results accurate to 9 decimal places, which is sufficient for most practical calculations.

What if I forget to press the 2ND key?

If you forget to press the 2ND key, the calculator will perform a square root operation instead of a cube root. Always double-check your function selection.

Can I use cube roots in equations on the TI-83?

Yes, you can use cube roots in equations by combining them with other operations as shown in the advanced usage section.