Square Root 2 Value | How to Find the Square Root of 2?
Last Updated :
23 Sep, 2024
Answer: The value or the square root of 2 = 1.414
Explanation:
The numerical value of square root 2 up to 50 decimal places is as follows:
√2 = 1.41421356237309504880168872420969807856967187537694…
The value of the square root of 2 is widely accepted as 1.414. The reason for this is that it contains an infinite number of decimals and to make mathematical computations easy, we use only 3 digits after decimal places.
Sometimes 99/70 is also used as a value for a Square Root of 2.
Let's learn the methods to find the square root of the 2 values in detail.
Square Root Calculator
How to Find the Square Root of 2?
Square root of a number is the value that when multiplied by itself, results in the number taken as input. To compute the square root, we must first check if the number is a perfect square. Perfect Squares are the numbers, the roots of which are whole numbers.
For example, 4, 9, 25, 36, 49, etc. It is easier to compute the square root of a perfect square number as compared to a non-perfect square number.
To compute the root of a non-perfect number, we usually apply one of these two methods:
- Long division Method
- Estimation Method (Guess and Check Method)
Value of Square Root 2 by Long Division Method
It is always easier to compute the square root of perfect squares. But to compute the square root of a non-perfect square, we need to perform the long division method.
To compute the square root of 2, we need to follow the steps given below:
Step 1: Write 2 as 2.000000 to make it easier to divide
Step 2: Now look for the perfect square less than 2 i.e. 1 and divide the number with it.
Step 3: Now the quotient and the remainder are 1. We will place a decimal in the quotient and bring down the pair of zeroes for further division.
Step 4: Now add the quotient with the existing divisor, this will become the digit at the tens place for our next divisor.
Step 5: For the unit's place, we need to find a value that can be placed at the unit place of both quotient and the divisor such that the new divisor when multiplied with the unit digit of the quotient results in the highest number less than the remainder.
Now. bring down the next pair of zeros and repeat the steps 4th and 5th. This can be done for infinite steps as the exact value of the square root of 2 goes up to infinite decimal places.
We can compute the result up to 4 decimal places as that can be used for approx. value of the square root.
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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.
Table of Square Root
Square roots of various numbers are widely used in mathematics. The table given below gives us the square root of various numbers which are used commonly.
| Number | Square Root |
|---|
| 1 | √(1) = 1 |
| 2 | √(2) = 1.414 (approx) |
| 3 | √(3) = 1.732 (approx) |
| 4 | √(4) = 2 |
| 5 | √(5) = 2.236(approx) |
| 9 | √(9) = 3 |
| 16 | √(16) = 4 |
| 25 | √(25) = 5 |
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