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Square Root Calculator

Square root of 5 is 2.2360679774998

Description

The Square Root Calculator allows you to easily find the square root of any non-negative number. Simply enter the value, and the calculator will provide the result instantly. This tool is perfect for students, professionals, or anyone who needs quick and accurate square root calculations without the need for a calculator. Additionally, you can learn how to calculate square roots manually to improve your math skills.

How to Use

  1. Enter a non-negative number in the input field. If no value is provided, the default value is 5.
  2. Click the "Calculate Square Root" button to see the result.
  3. The result will be displayed below the button, showing the square root of the input value.

How to Calculate the Square Root Manually

To calculate the square root of a number manually, you can use the following method. For example, let's calculate the square root of 5:

  1. Start by making an initial guess. A good first guess for the square root of 5 is half of it: 2.5.
  2. Apply the **Babylonian Method** (also known as **Newton's Method**):
    • Divide 5 by your guess.
    • Take the average of the guess and the result of the division.
    • For example, if your guess is 2.5:
      New guess = (2.5 + (5 / 2.5)) / 2 = 2.25.
  3. Repeat the process with the new guess until you reach the desired level of accuracy.
  4. This iterative process will provide you with an increasingly accurate estimate of the square root.

Examples of Squares and Square Roots

Here are some common examples of square roots:

  • Square root of 1 = 1
  • Square root of 4 = 2
  • Square root of 9 = 3
  • Square root of 16 = 4
  • Square root of 25 = 5
  • Square root of 36 = 6
  • Square root of 49 = 7
  • Square root of 64 = 8
  • Square root of 81 = 9
  • Square root of 100 = 10

Understanding these examples can help you estimate square roots more easily. For instance, if you need to find the square root of a number like 50, you know it must be between 7 (square root of 49) and 8 (square root of 64).

Last updated: 10/06/2024
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