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How to Put Nth Root in Calculator Ti84 Old

Reviewed by Calculator Editorial Team

Calculating nth roots on the TI-84 Plus calculator is straightforward once you know the correct sequence of steps. This guide will walk you through the process using both the calculator's built-in functions and manual methods.

Introduction

The TI-84 Plus calculator is a powerful tool for mathematical calculations, including finding nth roots. An nth root of a number x is a number y such that y^n = x. For example, the cube root of 27 is 3 because 3³ = 27.

This guide covers two methods for calculating nth roots on the TI-84 Plus:

  1. Using the calculator's built-in functions
  2. Manual calculation using logarithms

Both methods are explained in detail below with step-by-step instructions and examples.

Using the Calculator

Calculating nth roots on the TI-84 Plus is simple using the calculator's built-in functions. Here's how to do it:

Formula

To calculate the nth root of a number x, use the formula:

y = x^(1/n)

Step-by-Step Instructions

  1. Press the 2ND key and then the ^ key to access the exponent function.
  2. Enter the number you want to find the root of (x).
  3. Press the ^ key again.
  4. Enter the reciprocal of the root you want to find (1/n). For example, for a cube root, enter 1/3.
  5. Press the = key to get the result.

Example

Let's find the cube root of 27:

  1. Press 2ND then ^.
  2. Enter 27.
  3. Press ^.
  4. Enter 1/3.
  5. Press = to get the result: 3.

Note: The TI-84 Plus can handle both positive and negative numbers for x, but the root number n must be a positive integer.

Manual Calculation

If you prefer to calculate nth roots manually, you can use logarithms. Here's how:

Formula

To calculate the nth root of a number x using logarithms:

y = 10^((log(x)/n))

Step-by-Step Instructions

  1. Take the logarithm of the number x.
  2. Divide the result by the root number n.
  3. Calculate 10 raised to the power of the result from step 2.

Example

Let's find the cube root of 27 using logarithms:

  1. Calculate log(27) ≈ 1.4314.
  2. Divide by 3: 1.4314/3 ≈ 0.4771.
  3. Calculate 10^0.4771 ≈ 3.

Note: This method works for positive numbers only. For negative numbers, you'll need to use complex numbers, which the TI-84 Plus can handle but requires additional steps.

Common Errors

When calculating nth roots on the TI-84 Plus, you might encounter these common issues:

Incorrect Root Number

Entering the wrong root number (n) will give you the wrong result. For example, entering 1/2 instead of 1/3 for a cube root will give you a square root instead.

Negative Numbers

The TI-84 Plus can calculate roots of negative numbers, but the results will be complex numbers. Make sure you understand complex numbers if you're working with negative bases.

Non-integer Roots

The TI-84 Plus can handle non-integer roots, but the results might not be as precise as with integer roots. For more accurate results, consider using a scientific calculator or software.

FAQ

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

Yes, you can find the nth root of a negative number on the TI-84 Plus, but the result will be a complex number. The calculator will display the result in the form a + bi, where a and b are real numbers.

What if I enter a non-integer root number?

The TI-84 Plus can handle non-integer roots, but the results might not be as precise as with integer roots. For more accurate results, consider using a scientific calculator or software.

How do I clear the calculator after calculating a root?

To clear the calculator, press the CLEAR key. This will erase all entries and start a new calculation.