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Square Root of 17




What is square root of 17? Let’s explore the exact steps how to find square root of a number based on the below example

Finding the Square Root of 17:

  1. Initial Estimate: Begin with an estimate for the square root of 17. Since 42 = 16 and 52 = 25, a reasonable starting point might be between 4 and 5. Let’s choose 4.5 as a starting estimate.
  2. Divide the Number by the Estimate: Divide 17 by your initial estimate. So, 17 ÷ 4.5 ≈ 3.78.
  3. Calculate the Average: Find the average of the result from step 2 and your initial estimate. Add your initial estimate (4.5) to the result (3.78) and then divide by 2, giving (4.5 + 3.78) ÷ 2 ≈ 4.14.
  4. Use the Average as a New Estimate: Take the average calculated in step 3 and use it as your new estimate.
  5. Repeat the Process: Continue steps 2 through 4 using the new estimate. Each iteration should bring you closer to the actual square root of 17.
  6. 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 17, then your estimate is accurate.
  7. Continue Until Satisfied: Keep iterating until the squared estimate is as close to 17 as you need for your purposes, depending on the desired level of precision.
  8. Final Estimate: When you’ve achieved the necessary precision, your final estimate is the square root of 17 to that level of accuracy.

Representing the Square Root of 17 Mathematically:

  • As a Radical: Since 17 is not a perfect square, its square root is typically represented with the radical symbol: √17.
  • As an Approximate Decimal: If a decimal approximation is adequate, use the result from your iterations, for instance, √17 ≈ 4.14.
  • Using the Approximation Symbol: If representing it as an approximation, you might use the ≈ symbol, like √17 ≈ 4.14.
  • Scientific Notation or Interval Notation: These formats are less common for a number like 17 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 17 is often left in its radical form, √17, or approximated to a few decimal places. This is because √17 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:

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