Square root of 2 by division method

Learn and know how to find the value of square root of 2. As many of us don’t know the value of root 2. So now am going to explain the process for finding the square root of 2 value in division method. Now am going to explain you in finding the root 2 value up to 5 decimal places. Up to know if you don’t know the process of finding root 2 value then follow my steps.

square root of 2

In general square root of 2 is a number which if you multiply by itself then you have to get 2 as the answer. As 2 is not a perfect square we are not going to get root 2 value very easily. We have to follow the division process for finding the square root of 2 value. There is no other method for getting the value of root 2.

 

Steps for finding the Square root of 2 by division method:

We know that 2 can be written as 2.000000000000 i.e. 2=2.000000000000

square root of 2

 

Now take a perfect square number which is below 2. We know that the perfect square number below 2 is 1.

square root of 2

So write 1 in the divisor place and one more 1 in quotient place. Then subtract 1 from 2 the answer will be 1.

Next, carry down two zero’s and write after 1 and take the decimal point in quotient after 1.

square root of 2

 

Now double the quotient and write in divisor place opposite to 100.after 2 we have to take a number and that same number we have to take in quotient also. Here I took 4 after 2 and the same number I wrote in quotient also after the decimal point. Now multiply like this 24 × 4 = 96. Then subtract 96 from 100 and write remainder as 4.

square root of 2

Again carry down two zeros and write after 4, so now it becomes 400.

square root of 2

Now opposite to 400 write 28 which is double the quotient 1.4 (don’t count. here take only number i.e. 14).

After 28 we take one number the same number we have to write in quotient after 4. Here I took one so that we can multiply like this 281 × 1 = 281 which is less than 400. Now do subtraction and write remainder i.e. here the remainder is 119.

square root of 2

Next, carry down two zeros and write after 119, it becomes 11900.

square root of 2

Now opposite to 11900 write 282 which is double the quotient 1.41 (don’t count. here take only number i.e. 141).After 282 we take one number the same number we have to write in quotient after 1. Here I took 4 so that we can multiply like this 2824 × 4 = 11296 which is less than 11900. Now do subtraction and write remainder i.e. here the remainder is 604.

square root of 2

Next, carry down two zeros and write after 604, it becomes 60400.

square root of 2

Now opposite to 60400 write 2828 which is double the quotient 1.414 (don’t count. here take only number i.e. 1414).

After 2828 we take one number the same number we have to write in quotient after 4. Here I took 2 so that we can multiply like this 28282 × 2 = 56564 which is less than 60400. Now do subtraction and write remainder i.e. here the remainder is 3836.

square root of 2

Next, carry down two zeros and write after 3836, it becomes 383600.

square root of 2

Now opposite to 383600 write 28284 which is double the quotient 1.4142 (don’t count. here take only number i.e. 14142).

After 28284 we take one number the same number we have to write in quotient after 2. Here I took 1 so that we can multiply like this 282841 × 1 = 282841 which is less than 383600. Now do subtraction and write remainder i.e. here the remainder is 100759.

square root of 2

That’s it now we got the square root of 2 as 1.41421. we took root 2 value up to 5 decimal places. But in general square root of 2 value, it is enough to remember up to 3 decimal places i.e. root 2 value is 1.414.