square root of 20 - MathQuadrum

What is square root of 20? Let’s explore the exact steps how to find square root of a number based on the below example

Finding the Square Root of 20

Initial Estimate: Start by choosing an estimate for the square root of 20. Knowing that 4 squared equals 16 and 5 squared equals 25, a good initial guess is between 4 and 5. Let’s choose 4.5 as our starting point.
Divide the Number by the Estimate: Next, divide 20 by your estimate. In this case, 20 divided by 4.5 is approximately 4.44.
Calculate the Average: Then, calculate the average of your initial estimate and the division result. Add 4.5 (your initial estimate) to 4.44 (the division result), and divide the sum by 2. This gives us approximately 4.47.
Use the Average as a New Estimate: Now, use this average as your new estimate for the next calculation.
Repeat the Process: Continue repeating the process of dividing and averaging using your new estimate. Each round of calculation should bring you closer to the actual value that, when squared, results in 20.
Check for Accuracy: After several iterations, test the accuracy of your estimate. Square your estimate and see how close the result is to 20. If it’s very close, your estimate is accurate.
Continue Until Satisfied: Keep iterating until your squared estimate is as close to 20 as needed, depending on your required level of precision.
Final Estimate: Once you’ve reached the desired precision, this final estimate represents the value that, when squared, is approximately equal to 20.

Representing the Calculation Mathematically:

Without Using Square Root Notation: Since 20 is not a perfect square, its square root can be expressed as the value that, when squared, equals 20. This can also be expressed by breaking down 20 into 4 times 5, where 4 is a perfect square.
As an Approximate Decimal: For a decimal approximation, use the result from your iterative calculations, for example, the value that, when squared, is approximately equal to 20 might be around 4.47.
Using Approximation Symbol: When representing it as an approximation, you might express it as ‘the value that, when squared, is approximately 20’, like 4.47.
Other Notations: While less common for a number like 20, scientific notation or interval notation can be used in more advanced mathematical contexts.

In practical scenarios, especially where high precision isn’t crucial, this value is often approximated to a few decimal places, as 20 is an irrational number and cannot be exactly expressed as a fraction. Its decimal representation is non-repeating and non-terminating.

Explore variety of examples below:

General rules: How to Find Square Root of a Number

Practical examples:

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