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Calculating Negative Square Root on Ti83

Reviewed by Calculator Editorial Team

Calculating square roots on the TI-83 calculator is straightforward, but understanding how to handle negative square roots requires a few extra steps. This guide explains the mathematical principles behind square roots, how to calculate them on the TI-83, and provides practical examples to help you work with negative square roots effectively.

Understanding Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9. Every positive real number has two square roots: one positive and one negative. For instance, the square roots of 9 are 3 and -3.

On the TI-83 calculator, the square root function (√) always returns the principal (non-negative) square root. This means that √9 will display 3, not -3. To find negative square roots, you need to understand the mathematical relationship between square roots and multiplication.

Negative Square Roots

Negative square roots are simply the negative values of the positive square roots. For any positive number x, the negative square root is -√x. For example, the negative square root of 9 is -3 because -3 × -3 = 9.

On the TI-83 calculator, you can find the negative square root by first calculating the positive square root and then multiplying the result by -1. This two-step process ensures accuracy and helps you understand the relationship between positive and negative square roots.

Calculating on TI-83

To calculate a negative square root on the TI-83 calculator, follow these steps:

  1. Press the 2ND key and then the √ key to access the square root function.
  2. Enter the number for which you want to find the square root.
  3. Press the ) key to close the square root function.
  4. Press the × key to multiply the result by -1.
  5. Enter -1 and press the ENTER key to get the negative square root.

For example, to find the negative square root of 16:

  1. Press 2ND then √.
  2. Enter 16.
  3. Press ).
  4. Press ×.
  5. Enter -1 and press ENTER.

The calculator will display -4, which is the negative square root of 16.

Formula

The formula for the negative square root of a number x is:

-√x

Where √x is the principal (non-negative) square root of x.

This formula is implemented in the TI-83 calculator as described in the previous section. By first calculating the positive square root and then multiplying by -1, you can accurately find the negative square root of any positive number.

Worked Example

Let's calculate the negative square root of 25 using the TI-83 calculator.

  1. Press 2ND then √ to access the square root function.
  2. Enter 25.
  3. Press ) to close the square root function.
  4. Press × to multiply the result by -1.
  5. Enter -1 and press ENTER.

The calculator will display -5, which is the negative square root of 25. This is because 5 × 5 = 25, and -5 × -5 = 25.

FAQ

Can the TI-83 calculator find negative square roots directly?

No, the TI-83 calculator's square root function (√) only returns the principal (non-negative) square root. To find negative square roots, you need to multiply the positive square root by -1.

What happens if I try to find the square root of a negative number on the TI-83?

The TI-83 calculator will display an error message because the square root of a negative number is not a real number. It is an imaginary number, which involves the imaginary unit i (√-1 = i).

Is there a difference between the square root and the negative square root?

Yes, the square root of a number is always non-negative, while the negative square root is the negative value of the positive square root. For example, the square root of 16 is 4, and the negative square root is -4.

Can I use the TI-83 calculator to find square roots of fractions or decimals?

Yes, the TI-83 calculator can find square roots of fractions and decimals. Simply enter the fraction or decimal after pressing the square root function and follow the same steps for negative square roots if needed.

What if I make a mistake while entering the number for the square root?

If you make a mistake, press the CLEAR key to reset the calculator and start over. Double-check each step to ensure accuracy.