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Squre Root 3 on Ti Calculator

Reviewed by Calculator Editorial Team

Calculating the square root of 3 on a TI calculator is a common mathematical operation used in various fields including geometry, algebra, and trigonometry. This guide explains how to perform this calculation accurately using a TI calculator, provides the mathematical formula, and includes practical examples.

How to calculate square root 3 on TI calculator

To calculate the square root of 3 on a TI calculator, follow these steps:

  1. Turn on your TI calculator and ensure it's in the appropriate mode (usually "Math" or "Home" mode).
  2. Press the "2nd" function key to access the secondary functions.
  3. Press the "√" (square root) key to bring up the square root function.
  4. Enter the number "3" by pressing the "3" key.
  5. Press the ")" key to close the square root function.
  6. The calculator will display the result: √3 ≈ 1.73205080757.

Note: The exact value of √3 is an irrational number that cannot be expressed as a simple fraction. The decimal approximation provided by the calculator is accurate to 12 decimal places.

Formula used

The square root of a number x is a value that, when multiplied by itself, gives the original number. Mathematically, this is represented as:

√x = y where y × y = x

For x = 3:

√3 ≈ 1.73205080757

The square root function is an inverse operation of squaring. It's widely used in geometry to find the length of a side of a right triangle when the other two sides are known, in algebra to solve quadratic equations, and in trigonometry to find the lengths of sides in right triangles.

Examples

Example 1: Basic Calculation

Calculate √3 using a TI calculator:

  1. Press "2nd" then "√" to access the square root function.
  2. Enter "3" and press ")" to close the function.
  3. The calculator displays: 1.73205080757.

Example 2: Using in a Geometry Problem

Find the length of the hypotenuse of a right triangle with legs of 1 unit and √3 units:

  1. Calculate √3 ≈ 1.73205080757.
  2. Use the Pythagorean theorem: c = √(a² + b²) = √(1² + (√3)²) = √(1 + 3) = √4 = 2.
  3. The hypotenuse is 2 units long.

Example 3: Solving a Quadratic Equation

Solve the equation x² - 2x - 3 = 0:

  1. Use the quadratic formula: x = [2 ± √(4 + 12)] / 2 = [2 ± √16] / 2.
  2. Calculate √16 = 4.
  3. Solutions: x = (2 + 4)/2 = 3 and x = (2 - 4)/2 = -1.

FAQ

Q: What is the exact value of √3?
A: The exact value of √3 is an irrational number that cannot be expressed as a simple fraction. It's approximately 1.73205080757.
Q: How do I calculate √3 on a TI calculator?
A: Press "2nd" then "√", enter "3", and press ")" to get the result: √3 ≈ 1.73205080757.
Q: Where is the square root function located on a TI calculator?
A: The square root function is typically found by pressing "2nd" then "√" on most TI calculator models.
Q: Can I use the square root function for negative numbers?
A: No, the square root function on a TI calculator only works for non-negative numbers. Attempting to calculate the square root of a negative number will result in an error.