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How to Square Root A Fraction on Ti-84 Plus Calculator

Reviewed by Calculator Editorial Team

Calculating the square root of a fraction on your TI-84 Plus calculator is straightforward once you understand the proper steps. This guide will walk you through the process, including how to enter fractions and compute their square roots accurately.

Introduction

The TI-84 Plus calculator is a powerful tool for mathematical calculations, including operations with fractions. Calculating the square root of a fraction involves understanding how to input fractions and perform the square root operation correctly.

This guide provides step-by-step instructions for entering a fraction and computing its square root on your TI-84 Plus calculator. We'll also include a worked example to demonstrate the process clearly.

Method: Square Root of a Fraction

The square root of a fraction can be calculated using the following formula:

√(a/b) = √a / √b

This means you can take the square root of the numerator and the denominator separately, then divide the results.

On the TI-84 Plus calculator, you'll need to enter the fraction in the correct format and use the square root function to compute the result.

Step-by-Step Instructions

  1. Enter the Fraction

    To enter a fraction on your TI-84 Plus calculator, follow these steps:

    1. Press the MATH key.
    2. Use the arrow keys to highlight the Frac option.
    3. Press ENTER to select the fraction template.
    4. Enter the numerator (top number) of your fraction.
    5. Press the / key to enter the denominator (bottom number).
    6. Enter the denominator.
    7. Press ENTER to confirm the fraction.

  2. Calculate the Square Root

    Once you've entered the fraction, follow these steps to calculate its square root:

    1. Press the 2ND key.
    2. Press the √ key to access the square root function.
    3. The calculator will display the square root of your fraction.

  3. Simplify the Result

    If the result is a fraction, you can simplify it by rationalizing the denominator:

    1. Multiply the numerator and denominator by the square root of the denominator.
    2. Simplify the resulting fraction.

Worked Example

Let's calculate the square root of the fraction 9/16 using the TI-84 Plus calculator.

  1. Enter the Fraction

    Follow the steps above to enter the fraction 9/16.

  2. Calculate the Square Root

    Press 2ND followed by √. The calculator will display:

    √(9/16) = 3/4

  3. Verification

    To verify the result, you can calculate the square of 3/4:

    (3/4)² = 9/16

    This confirms that the square root of 9/16 is indeed 3/4.

Frequently Asked Questions

How do I enter a fraction on my TI-84 Plus calculator?
To enter a fraction, press the MATH key, select the Frac option, enter the numerator and denominator, and press ENTER.
Can I calculate the square root of a mixed number on the TI-84 Plus?
Yes, you can convert the mixed number to an improper fraction first, then follow the same steps to calculate its square root.
What if the square root of my fraction is an irrational number?
The TI-84 Plus will display the exact form of the square root. For example, √(2/3) will show as √(2)/√(3).
How do I simplify a complex fraction result?
Multiply the numerator and denominator by the square root of the denominator to rationalize it, then simplify the resulting fraction.