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How to Use A Graphing Calculator to Use Squar Root

Reviewed by Calculator Editorial Team

Calculating square roots on a graphing calculator is a fundamental math skill that's useful in algebra, geometry, and many other areas of mathematics. This guide will walk you through the process step by step, using a built-in calculator to demonstrate the technique.

Introduction

Graphing calculators are powerful tools that can perform complex mathematical operations with ease. One of the most basic but essential functions is calculating square roots. The square root of a number is a value that, when multiplied by itself, gives the original number.

Square Root Formula

For a number \( x \), the square root is written as \( \sqrt{x} \). The formula is:

\( \sqrt{x} = y \) where \( y \times y = x \)

Graphing calculators typically have a dedicated square root function that makes this calculation quick and easy. In this guide, we'll explore how to use this function effectively.

Graphing Calculator Basics

Before we dive into square roots, let's review some basic graphing calculator operations that will help you understand how to use the square root function.

Turning On the Calculator

Most graphing calculators have a power button that turns the device on and off. Locate this button and press it to activate your calculator.

Navigating the Menu

Graphing calculators typically have a menu system that allows you to access different functions. Use the arrow keys to navigate through the menu options.

Entering Numbers

To enter numbers, use the number pad on the calculator. For decimal numbers, use the decimal point button.

Using the Square Root Function

The square root function is usually located in the math or function menu. Look for a button labeled "√" or "sqrt".

Square Root Function

The square root function is one of the most commonly used functions on a graphing calculator. It allows you to quickly find the square root of any positive number.

Accessing the Square Root Function

To access the square root function, follow these steps:

  1. Turn on your graphing calculator.
  2. Navigate to the math or function menu.
  3. Locate the square root function (√ or sqrt).
  4. Press the function key to select it.

Entering the Number

Once you've selected the square root function, enter the number you want to find the square root of. For example, if you want to find the square root of 25, enter "25".

Calculating the Result

After entering the number, press the equals (=) button to calculate the result. The calculator will display the square root of the number you entered.

Note

Most graphing calculators will display the result in decimal form. If you need an exact fraction, you may need to use the fraction function or convert the decimal to a fraction manually.

Step-by-Step Guide

Let's walk through a complete example of using the square root function on a graphing calculator.

Example: Finding the Square Root of 36

  1. Turn on your graphing calculator.
  2. Navigate to the math or function menu.
  3. Locate the square root function (√ or sqrt).
  4. Press the function key to select it.
  5. Enter the number "36" using the number pad.
  6. Press the equals (=) button to calculate the result.
  7. The calculator will display "6" as the result.

This means that 6 × 6 = 36, so the square root of 36 is 6.

Example: Finding the Square Root of 50

  1. Turn on your graphing calculator.
  2. Navigate to the math or function menu.
  3. Locate the square root function (√ or sqrt).
  4. Press the function key to select it.
  5. Enter the number "50" using the number pad.
  6. Press the equals (=) button to calculate the result.
  7. The calculator will display "7.0710678118654755" as the result.

This means that 7.0710678118654755 × 7.0710678118654755 ≈ 50.

Worked Examples

Let's look at a few more examples to reinforce what we've learned.

Example 1: Square Root of 100

Using the square root function:

  1. Select √ from the math menu.
  2. Enter "100".
  3. Press =.
  4. Result: 10

Example 2: Square Root of 16

Using the square root function:

  1. Select √ from the math menu.
  2. Enter "16".
  3. Press =.
  4. Result: 4

Example 3: Square Root of 2

Using the square root function:

  1. Select √ from the math menu.
  2. Enter "2".
  3. Press =.
  4. Result: 1.414213562373095

This is an irrational number, which means it cannot be expressed as a simple fraction and has an infinite non-repeating decimal expansion.

Troubleshooting

If you're having trouble using the square root function on your graphing calculator, here are some common issues and solutions:

Issue: Calculator Doesn't Respond

Solution: Make sure the calculator is turned on and that you're pressing the correct buttons. If the problem persists, try turning the calculator off and on again.

Issue: Incorrect Result

Solution: Double-check that you've entered the correct number and that you've selected the square root function. If you're still getting an incorrect result, try clearing the calculator and starting over.

Issue: Function Not Found

Solution: Consult your calculator's manual to locate the square root function. Different models may have slightly different menu structures.

Tip

If you're still having trouble, consider practicing with a different calculator or seeking help from a teacher or tutor.

FAQ

What is the square root function used for?
The square root function is used to find a number that, when multiplied by itself, gives the original number. It's essential in algebra, geometry, and many other areas of mathematics.
Can I find the square root of negative numbers?
No, most graphing calculators cannot find the square root of negative numbers. The square root of a negative number is an imaginary number, which requires complex number operations.
How do I clear the calculator after using the square root function?
Most graphing calculators have a clear (CLR) or delete (DEL) button that you can use to clear the calculator after performing calculations.
Can I use the square root function with variables?
Yes, many graphing calculators allow you to use the square root function with variables. For example, you can enter √(x) to find the square root of a variable.
What should I do if the square root function isn't working?
If the square root function isn't working, try turning the calculator off and on again. If the problem persists, consult your calculator's manual or seek help from a teacher or tutor.