The square root of 2 or root 2 is represented using the square root symbol √ and written as √2 whose value is 1.414. This value is widely used in mathematics. Root 2 is an irrational number as it cannot be expressed as a fraction and has an infinite number of decimals. So, the exact value of the root of 2 cannot be determined.
Root 2 Value
The square root of 2 is the number which when multiplied with itself gives the result as 2. It is generally represented as √2 or 2½. The numerical value of square root 2 up to 50 decimal places is as follows:
|√2 = 1.41421356237309504880168872420969807856967187537694…|
At present, the root 2 value is computed to 10 trillion digits. For general use, its value is truncated and is used as 1.414 to make calculations easy. The fraction 99/70 is also sometimes used as the value of √2.
How to Find Square Root 2
To find the square root value of a number, we usually check if the number is a perfect square or not. It is easy to find the root of perfect squares, but for non-perfect squares, we have to use the long division method to find the root value. Numbers like 2, 3, 5, 20, etc. are non-perfect squares, but 4, 9, 25, etc. are perfect squares, which gives the whole number when we take the root of them.
Value of Square Root of 2 by Long Division Method
Now, how to find the square root of 2 by division method. The first thing that you can try is the popular division method. The steps involved in this method are:
- Step 1: In this method, you have to make an estimate first, means you have chosen a close number by finding at-least two roots which are perfect. It has been those root that your number is between those values.
- Step 2: Then, you can divide the number by one of those square roots.
- Step 3: Once you start and continue with the division process, you will need to take the average of the result of step 2 and the root. And finally, you can use the result that you get in step 3 to repeat the 2nd and 3rd step until you get a number that is satisfactory or accurate enough for you. The example is given below:
Also, try this square root calculator which is an online tool that shows root for any given input. If you put the input as 2 then the tool quickly displays the result for the given number which is 1.414. Additionally, you can also check this BYJU’S video lesson to learn how to find the square of any number.