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Calculating Negative Square Root on Ti 83

Reviewed by Calculator Editorial Team

The TI-83 calculator is a powerful tool for performing mathematical operations, including square roots. This guide explains how to calculate negative square roots on the TI-83, including the proper formula, step-by-step instructions, and practical examples.

Introduction

The square root of a number is a value that, when multiplied by itself, gives the original number. For positive numbers, there are two square roots: one positive and one negative. The TI-83 calculator can compute both positive and negative square roots, though it primarily displays the principal (positive) square root by default.

Calculating negative square roots on the TI-83 requires understanding how the calculator handles complex numbers and how to access the negative root when needed.

Square Root Formula

The square root of a number \( x \) is given by the formula:

Square Root Formula

For a positive number \( x \), the square roots are \( \sqrt{x} \) and \( -\sqrt{x} \).

The principal square root (positive root) is typically displayed by default.

For negative numbers, the square root involves imaginary numbers. The formula for the square root of a negative number \( -x \) is:

Negative Square Root Formula

\( \sqrt{-x} = i\sqrt{x} \), where \( i \) is the imaginary unit (\( i^2 = -1 \)).

TI-83 Calculator Steps

To calculate negative square roots on the TI-83, follow these steps:

  1. Press the MATH key.
  2. Use the arrow keys to highlight the NUM option.
  3. Press the 2nd key to select the √x function.
  4. Enter the number for which you want to find the square root.
  5. Press the ENTER key to display the result.

Note

The TI-83 will display the principal (positive) square root by default. To find the negative square root, multiply the result by -1.

Worked Examples

Example 1: Positive Square Root

Find the square roots of 25.

  1. Press MATH → NUM → 2nd → √x.
  2. Enter 25.
  3. Press ENTER.

The calculator displays 5 (the positive square root). The negative square root is -5.

Example 2: Negative Square Root

Find the square root of -9.

  1. Press MATH → NUM → 2nd → √x.
  2. Enter -9.
  3. Press ENTER.

The calculator displays 3i (the principal square root of -9). The negative square root is -3i.

Frequently Asked Questions

Can the TI-83 calculate negative square roots directly?

The TI-83 primarily displays the principal (positive) square root. To find the negative square root, multiply the result by -1.

What is the difference between √x and 2nd √x on the TI-83?

√x calculates the principal square root, while 2nd √x calculates the square root of the negative of the input. For example, √(-4) gives an error, but 2nd √(-4) gives 2i.

How do I handle complex numbers on the TI-83?

The TI-83 represents complex numbers with the letter "i" for the imaginary unit. For example, the square root of -1 is displayed as "i".