Square Root 2 Value by Estimation Method
In the Estimation Method for calculating the square root of 2 involves, we make an initial guess and then refine it to get closer to the actual value.
Let’s discuss how it works.
- Begin with a reasonable guess for the square root of 2. A common starting point is 1, because 12 = 1, which is close to 2.
- Use the following formula to improve your guess:
New Estimate = (Old Estimate + 2 ∕Old Estimate) ∕ 2
3. Repeat the refining step using the new estimate as the old estimate in the next iteration.
Example:
- Start with 1 as the initial guess.
- Apply Formula: New Estimate = (1 + 2/1) / 2 = 1.5.
- Use 1.5 as the new estimate and apply the formula again: New Estimate = (1.5 + 2/1.5) / 2 ≈ 1.4167.
- Continue this process until the estimate squares to a value as close to 2 as needed for your precision requirements.
With each iteration, our estimate will get closer to the actual square root of 2.
Root 2 Value | How to Find the Square Root of 2?
Square root of 2 is represented as √2 or 2½. When multiplied by itself, √2 will result in the number 2. The value of the square root of 2 is 1.414.
Let’s learn the methods to find the square root of the 2 values in detail.
Table of Content
- Root 2 Value
- How to Find the Square Root of 2?
- Square Root 2 Value by Long Division Method
- Square Root 2 Value by Estimation Method
- Is Square Root of 2 Rational or Irrational?
- Root 2 Value Calculation- FAQs