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How to Write Square Root 3 on A Calculator

Reviewed by Calculator Editorial Team

Writing square roots on calculators can be confusing for beginners. This guide explains how to properly input √3 (the square root of 3) on scientific, graphing, and basic calculators, with step-by-step instructions and a built-in calculator tool.

How to Enter √3 on Different Calculators

The method for entering square roots varies by calculator type. Scientific and graphing calculators have dedicated keys, while basic calculators require manual entry. Here's how to do it on each type:

Formula: √a = a^(1/2)

This means the square root of any number is equivalent to raising that number to the power of 1/2.

Note: Always ensure your calculator is in the correct mode (usually "DEG" for degrees or "RAD" for radians) before entering square roots, as this affects trigonometric functions.

Scientific Calculators

Scientific calculators have a dedicated square root key (often labeled √ or x²). Here's how to enter √3:

  1. Press the "√" key (usually located near the "x²" key)
  2. Enter the number 3
  3. Press "=" to see the result (approximately 1.73205)

Alternatively, you can use the exponent function:

  1. Enter the number 3
  2. Press the "xʸ" key (exponent function)
  3. Enter 1/2
  4. Press "=" to get the same result

Graphing Calculators

Graphing calculators like the TI-84 have similar functionality to scientific calculators:

  1. Press the "2nd" key
  2. Press the "√" key (which appears as "x√" on the screen)
  3. Enter the number 3
  4. Press ")" to close the parentheses
  5. Press "ENTER" to see the result

For the exponent method:

  1. Enter the number 3
  2. Press the "^" key
  3. Enter 1/2
  4. Press "ENTER" to get the result

Basic Calculators

Basic calculators don't have a square root key, so you'll need to use the exponent method:

  1. Enter the number 3
  2. Press the "xʸ" key (or "yˣ" depending on your calculator)
  3. Enter 1/2
  4. Press "=" to see the result

If your basic calculator doesn't have an exponent function, you'll need to use the square root approximation method:

  1. Calculate 3/2 = 1.5
  2. Calculate 3/1.5 = 2.0
  3. Average these two results: (1.5 + 2.0)/2 = 1.75
  4. Repeat the process using 1.75 as your new guess

Examples of Square Root Calculations

Here are some practical examples of square root calculations:

Expression Result Use Case
√9 3 Finding the side length of a square with area 9
√16 4 Calculating the radius of a circle with area 16π
√3 ≈1.732 Used in trigonometry and geometry calculations

For more complex calculations, you might need to use the calculator's memory functions or store intermediate results.

Frequently Asked Questions

Q: Why does my calculator show a different result for √3 than the one I see in textbooks?
A: Calculators typically display results to about 10 decimal places, while textbooks often show rounded values. The actual value of √3 is an irrational number that continues infinitely without repeating.
Q: Can I calculate cube roots on my calculator?
A: Yes, using the same exponent method. For the cube root of 3, you would enter 3^(1/3). Most scientific calculators have a dedicated cube root key (³√) as well.
Q: What if I get an error when trying to calculate √3?
A: Common errors include forgetting to close parentheses on graphing calculators or entering the wrong mode. Double-check your input and ensure your calculator is in the correct mode (usually "DEG" or "RAD").
Q: Is there a way to calculate square roots without a calculator?
A: Yes, you can use the approximation method described in the basic calculator section, though it's less precise than using a calculator.