square root of 125 - MathQuadrum

What is square root of 125? Let’s explore the exact steps how to find square root of a number based on the below example

Finding the Square Root of 125

Initial Estimate

Begin with an estimate. Since 10² (10 x 10) equals 100 and 11² (11 x 11) equals 121, a good starting point is between 10 and 11. We’ll choose 11 as our starting estimate.

Divide the Number by the Estimate

Divide 125 by your initial estimate: 125 ÷ 11 ≈ 11.36.

Calculate the Average

Find the average of the result from step 2 and your initial estimate: (11 + 11.36) ÷ 2 ≈ 11.18.

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, getting closer to the actual square root of 125.

Check for Accuracy

After a few iterations, check the accuracy by squaring your estimate. If it’s close to 125, your estimate is accurate.

Continue Until Satisfied

Keep iterating until the squared estimate is close enough to 125 for your purposes, depending on your desired precision.

Final Estimate

When you’ve achieved the necessary precision, your final estimate is the square root of 125 to that level of accuracy.

Representing the Square Root of 125 Mathematically

As a radical: √125. This can be simplified to 5√5 because 125 can be expressed as 25 x 5, and 25 is a perfect square.
As an approximate decimal: √125 ≈ 11.18.
Using the approximation symbol: √125 ≈ 11.18.
Scientific Notation or Interval Notation can be used in more advanced contexts.

In practical scenarios, especially when high precision is not crucial, the square root of 125 is often left in its simplified radical form, 5√5, or approximated to a few decimal places.

Explore variety of examples below:

General rules: How to Find Square Root of a Number

Practical examples:

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