Square Root of 12 - MathQuadrum

What is square root of 12? Let’s explore the exact steps how to find square root of a number based on the below example

Finding the Square Root of 12

Initial Estimate: Choose a starting estimate for the square root of 12. A logical choice might be between 3 and 4, as 3² = 9 and 4² = 16. Let’s start with 3.5 as an estimate.
Divide the Number by the Estimate: Divide 12 by your initial estimate. So, 12 ÷ 3.5 ≈ 3.43.
Calculate the Average: Find the average of the result from step 2 and your initial estimate. Add your initial estimate (3.5) to the result (3.43) and then divide by 2, which gives (3.5 + 3.43) ÷ 2 ≈ 3.47.
Use the Average as a New Estimate: Take the average calculated in step 3 as your new estimate.
Repeat the Process: Continue steps 2 through 4 using the new estimate. Each iteration should bring you closer to the actual square root of 12.
Check for Accuracy: After a few iterations, check the accuracy of your estimate by squaring it. If the square of your estimate is close to 12, then your estimate is accurate.
Continue Until Satisfied: Keep iterating until the squared estimate is as close to 12 as you need for your purposes, depending on the desired level of precision.
Final Estimate: When you’ve achieved the necessary precision, your final estimate is the square root of 12 to that level of accuracy.

Representing the Square Root of 12 Mathematically:

As a Radical: Since 12 is not a perfect square, its square root is typically represented with the radical symbol: √12. This can be simplified to 2√3 because 12 = 4 × 3 and 4 is a perfect square.
As an Approximate Decimal: If a decimal approximation is adequate, use the result from your iterations, for instance, √12 ≈ 3.47.
Using the Approximation Symbol: If representing it as an approximation, you might use the ≈ symbol, like √12 ≈ 3.47.
Scientific Notation or Interval Notation: These formats are less common for a number like 12 but can be utilized in more advanced or specific mathematical contexts.

In practical scenarios, especially when high precision is not crucial, the square root of 12 is often left in its simplified radical form, 2√3, or approximated to a few decimal places. This is because √12 is an irrational number, meaning it cannot be expressed exactly as a fraction, and 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:

Return to MathQuadrum.com from What is square root of 12 home for more topics on mathematics