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How to Put Cubed Root in Calculator Ti-89

Reviewed by Calculator Editorial Team

Calculating cubed roots on the TI-89 calculator is straightforward once you know the correct steps. This guide will walk you through the process, explain the formula used, and provide a worked example to help you understand how to use this function effectively.

Introduction

The TI-89 is a powerful graphing calculator that can perform a wide range of mathematical operations, including calculating roots. The cubed root of a number is a value that, when multiplied by itself three times, gives the original number. In mathematical terms, the cubed root of a number \( x \) is \( x^{1/3} \).

This guide will show you how to calculate cubed roots on your TI-89 calculator using the built-in functions. Whether you're a student studying algebra or a professional working with advanced mathematics, knowing how to use your calculator efficiently can save you time and reduce errors.

Steps to Calculate Cubed Root on TI-89

Follow these steps to calculate the cubed root of a number using your TI-89 calculator:

  1. Turn on your TI-89 calculator and ensure it's in the correct mode for your needs.
  2. Press the [2ND] key to access the secondary functions.
  3. Press the [MATH] key to open the math menu.
  4. Scroll down to the [A] option and press [ENTER]. This selects the "a" function, which is used for roots.
  5. Enter the number for which you want to calculate the cubed root. For example, if you want to find the cubed root of 27, type "27".
  6. Press the [,] key to enter the exponent. For a cubed root, the exponent is 1/3.
  7. Type "1/3" and press [ENTER].
  8. The calculator will display the result, which is the cubed root of the number you entered.

Tip: If you're working with negative numbers, the TI-89 will calculate the real root. For example, the cubed root of -8 is -2.

Formula Used

The formula for calculating the cubed root of a number \( x \) is:

Cubed Root of \( x \) = \( x^{1/3} \)

This formula is derived from the definition of roots. A root of a number is a value that, when raised to a certain power, gives the original number. For a cubed root, the power is 1/3.

For example, the cubed root of 27 is 3 because \( 3^3 = 27 \). Similarly, the cubed root of 64 is 4 because \( 4^3 = 64 \).

Worked Example

Let's work through an example to see how to calculate the cubed root of 125 using the TI-89 calculator.

  1. Turn on your TI-89 calculator and ensure it's in the correct mode.
  2. Press the [2ND] key to access the secondary functions.
  3. Press the [MATH] key to open the math menu.
  4. Scroll down to the [A] option and press [ENTER].
  5. Enter the number "125".
  6. Press the [,] key to enter the exponent.
  7. Type "1/3" and press [ENTER].
  8. The calculator will display the result, which is 5.

This is because \( 5^3 = 125 \), so the cubed root of 125 is indeed 5.

Note: The TI-89 calculator will display the result in decimal form if the exact root is not an integer. For example, the cubed root of 10 will be approximately 2.15443.

Frequently Asked Questions

Can I calculate the cubed root of a negative number on the TI-89?

Yes, you can calculate the cubed root of a negative number on the TI-89. The calculator will display the real root. For example, the cubed root of -27 is -3.

What if I enter a non-integer exponent for the root?

If you enter a non-integer exponent, the TI-89 will calculate the root accordingly. For example, if you enter 27 and 1/4 as the exponent, the calculator will display the fourth root of 27, which is approximately 2.27951.

How do I clear the previous calculation on the TI-89?

To clear the previous calculation, press the [CLEAR] key on the TI-89. This will reset the calculator and allow you to start a new calculation.