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How to Get The Square Root of 2 on Calculator

Reviewed by Calculator Editorial Team

Calculating the square root of 2 is a fundamental mathematical operation that appears in many areas of mathematics, physics, and engineering. This guide will show you how to perform this calculation accurately using a calculator.

How to Calculate the Square Root of 2

The square root of a number is a value that, when multiplied by itself, gives the original number. For 2, this means finding a number that when multiplied by itself equals 2.

Most scientific calculators have a dedicated square root function that makes this calculation quick and easy. Here's how to use it:

  1. Turn on your calculator and clear any previous calculations.
  2. Enter the number 2.
  3. Press the square root button (often labeled with √).
  4. Read the result displayed on the calculator screen.

Note: If your calculator doesn't have a dedicated square root button, you can calculate it using the exponent function (yˣ) by entering 2 and then 0.5 as the exponent.

Step-by-Step Guide

Using a Scientific Calculator

  1. Locate the square root function on your calculator. It's typically represented by the √ symbol.
  2. Press the number 2 on your calculator.
  3. Press the √ button.
  4. The calculator will display the result: approximately 1.41421356237.

Using a Graphing Calculator

  1. Open your graphing calculator application.
  2. Enter the expression √(2) in the input field.
  3. Execute the calculation (usually by pressing Enter or a similar key).
  4. The result will appear on the screen.

Using a Programming Calculator

  1. Open your programming calculator.
  2. Enter the number 2.
  3. Use the square root function (often found in the math functions menu).
  4. The result will be displayed.

The Formula

The square root of a number x is mathematically represented as:

√x = y

where y × y = x

For the specific case of 2:

√2 ≈ 1.41421356237

This value is an irrational number, meaning it cannot be expressed as a simple fraction and its decimal representation goes on infinitely without repeating.

Worked Example

Let's walk through a practical example to see how this calculation works in a real-world context.

Example: Finding the Diagonal of a Square

Suppose you have a square with each side measuring 2 units. To find the length of the diagonal (d) of this square, you can use the Pythagorean theorem:

d = √(a² + b²)

where a and b are the lengths of the sides

Since both sides are equal (2 units), the calculation becomes:

d = √(2² + 2²) = √(4 + 4) = √8 ≈ 2.8284

This shows how the square root of 2 appears in geometric calculations.

Frequently Asked Questions

What is the square root of 2?
The square root of 2 is approximately 1.41421356237. It's an irrational number that cannot be expressed as a simple fraction.
How do I calculate the square root of 2 on a calculator?
Enter the number 2, then press the square root button (√). The calculator will display the result.
Why is the square root of 2 important?
The square root of 2 is important in mathematics, physics, and engineering. It appears in many geometric calculations and is a fundamental value in trigonometry.
Can I calculate the square root of 2 without a calculator?
Yes, you can use the long division method or other algebraic techniques, but a calculator provides a quick and accurate result.
Is the square root of 2 a whole number?
No, the square root of 2 is not a whole number. It's an irrational number with an infinite non-repeating decimal representation.