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How to Get Fourth Root on Calculator Ti84

Reviewed by Calculator Editorial Team

Calculating the fourth root of a number is a common mathematical operation, especially in fields like engineering and physics. The TI-84 calculator provides several methods to perform this calculation, either directly or through intermediate steps. This guide will walk you through the most efficient methods to get the fourth root on your TI-84 calculator.

Introduction

The fourth root of a number x is a value that, when raised to the power of 4, gives x. Mathematically, it's represented as:

x^(1/4) = y

where y^4 = x

For example, the fourth root of 16 is 2 because 2^4 = 16. The TI-84 calculator can compute this directly or through intermediate steps using logarithms and exponents.

Using the TI-84 Calculator

Method 1: Direct Calculation

  1. Press the 2ND key, then the ^ key to access the exponent function.
  2. Enter the number you want to find the fourth root of.
  3. Press the ^ key again.
  4. Enter 1/4 (the fraction one-fourth).
  5. Press ENTER to see the result.

Method 2: Using Logarithms

  1. Press the 2ND key, then the LN key to access the natural logarithm function.
  2. Enter the number you want to find the fourth root of.
  3. Press ENTER to calculate the natural logarithm.
  4. Press the 2ND key, then the ^ key to access the exponent function.
  5. Enter the result from step 3.
  6. Press the ÷ key.
  7. Enter 4.
  8. Press ENTER to get the logarithm of the fourth root.
  9. Press the 2ND key, then the LN key to access the natural logarithm function.
  10. Press the 2ND key, then the ^ key to access the exponent function.
  11. Press the e^x key (which is the 2ND key followed by the LN key again).
  12. Press ENTER to get the fourth root.

Note: The direct method (Method 1) is simpler and more accurate for most cases. The logarithmic method (Method 2) is useful when you need to understand the underlying mathematical process.

Manual Calculation Method

If you prefer to calculate the fourth root manually, you can use the following formula based on logarithms:

x^(1/4) = e^(ln(x)/4)

Here's how to apply this formula:

  1. Take the natural logarithm of the number x.
  2. Divide the result by 4.
  3. Calculate the exponential of the result to get the fourth root.

This method is particularly useful when using a calculator that doesn't have a direct fourth root function.

Worked Example

Let's find the fourth root of 81 using the TI-84 calculator.

Using Method 1 (Direct Calculation)

  1. Press 2ND then ^.
  2. Enter 81.
  3. Press ^ again.
  4. Enter 1/4.
  5. Press ENTER.

The calculator displays 3, which is the fourth root of 81.

Using Method 2 (Logarithmic Method)

  1. Press 2ND then LN.
  2. Enter 81.
  3. Press ENTER to get the natural logarithm (~4.3944).
  4. Press 2ND then ^.
  5. Enter the result from step 3.
  6. Press ÷.
  7. Enter 4.
  8. Press ENTER to get the logarithm of the fourth root (~1.0986).
  9. Press 2ND then LN.
  10. Press 2ND then ^.
  11. Press e^x (which is 2ND then LN again).
  12. Press ENTER to get the fourth root (~3).

The result is the same as with the direct method, confirming the accuracy of both approaches.

Frequently Asked Questions

Can I find the fourth root of a negative number on the TI-84?

No, the TI-84 calculator does not support finding the fourth root of negative numbers because it involves complex numbers. The fourth root of a negative number is not a real number.

Is there a difference between the fourth root and the square root of the square root?

Yes, there is a difference. The fourth root of a number is equivalent to the square root of the square root of the number. However, calculating it directly using the exponent 1/4 is more efficient and accurate.

How do I clear the calculator after performing a fourth root calculation?

Press the CLEAR key to clear the current calculation and start fresh. Alternatively, press the ON key to reset the calculator completely.

Can I use the TI-84 to find the fourth root of a fraction?

Yes, you can enter fractions directly into the TI-84 calculator. For example, to find the fourth root of 1/16, enter 1/16 and follow the steps for calculating the fourth root.

What if the TI-84 displays an error when calculating the fourth root?

Errors can occur if you enter an invalid input, such as a negative number or a non-numeric value. Double-check your input and ensure you're using the correct method for the type of number you're working with.