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How to Use The Square Root on The Ti-84 Calculator

Reviewed by Calculator Editorial Team

Calculating square roots on the TI-84 calculator is a fundamental skill for students and professionals working with mathematical problems. This guide provides step-by-step instructions, examples, and a built-in calculator to help you master this essential function.

How to Calculate Square Roots on TI-84

The TI-84 calculator provides several methods to calculate square roots. The most common approach uses the square root function (√) available in the math menu. This function can handle both positive and negative numbers, returning the principal (non-negative) square root.

Formula: √x = y where y² = x and y ≥ 0

For example, √16 = 4 and √9 = 3. The calculator will display an error if you attempt to calculate the square root of a negative number in real number mode.

Step-by-Step Guide

Method 1: Using the Square Root Function

  1. Press the 2ND key (top row, second from the left).
  2. Press the √ key (top row, second from the right). This will display "√(" on the screen.
  3. Enter the number you want to find the square root of. For example, type "16".
  4. Press the ) key to close the parentheses.
  5. Press ENTER to calculate the result. The calculator will display "4".

Method 2: Using the Exponent Function

  1. Enter the number you want to find the square root of. For example, type "16".
  2. Press the ^ key (top row, third from the right).
  3. Enter "0.5" (which is equivalent to 1/2).
  4. Press ENTER to calculate the result. The calculator will display "4".

Tip: The exponent method is useful when you need to calculate roots other than square roots, such as cube roots (using exponent 1/3).

Worked Examples

Let's look at a few examples to illustrate how to use the square root function on the TI-84 calculator.

Example 1: Simple Square Root

Calculate √25.

  1. Press 2ND then √ to display "√(".
  2. Type "25".
  3. Press ) then ENTER.
  4. The calculator displays "5".

Example 2: Decimal Square Root

Calculate √2.25.

  1. Press 2ND then √ to display "√(".
  2. Type "2.25".
  3. Press ) then ENTER.
  4. The calculator displays "1.5".

Example 3: Negative Number

Attempt to calculate √-9.

  1. Press 2ND then √ to display "√(".
  2. Type "-9".
  3. Press ) then ENTER.
  4. The calculator displays "ERROR: INVALID".

This error occurs because the square root of a negative number is not a real number. For complex numbers, you would need to use the complex number mode on the TI-84.

Common Mistakes

When using the square root function on the TI-84 calculator, there are several common mistakes to avoid:

1. Forgetting to Close Parentheses

If you forget to press the ) key after entering the number, the calculator will not calculate the square root correctly. Always ensure you close the parentheses after entering the number.

2. Using the Wrong Function

Confusing the square root function with the square function can lead to incorrect results. The square function is accessed by pressing x² (2ND then x²), which squares the number rather than finding its square root.

3. Attempting to Find Square Roots of Negative Numbers

As mentioned earlier, the TI-84 calculator in real number mode cannot calculate the square root of negative numbers. If you need to work with complex numbers, you will need to enable complex number mode.

4. Not Pressing ENTER

After entering the expression, always press ENTER to calculate the result. Forgetting to press ENTER will leave the expression on the screen without displaying the result.

Frequently Asked Questions

Can I find the square root of a negative number on the TI-84?
No, the TI-84 calculator in real number mode cannot calculate the square root of negative numbers. For complex numbers, you would need to enable complex number mode.
How do I clear the square root function from the screen?
Press the CLEAR key (bottom row, second from the left) to clear the current expression from the screen.
Can I use the square root function with variables?
Yes, you can use the square root function with variables. For example, if you have a variable X, you can calculate √X by pressing 2ND then √, typing "X", pressing ), and then ENTER.
What if I get an error when calculating a square root?
If you receive an error, double-check that you have entered the number correctly and closed the parentheses. Also, ensure you are not trying to calculate the square root of a negative number in real number mode.