What is the approximate value of

The correct answer is: 3.5

So now we have given the number , lets go by long division method:
First we have to make a pair from right side, the unit side.
Then we have to find a number which when multiplied to itself gives the product which is less than 12. So it is 3 x 3 = 9. Divide 12 by 3 now.
Now to continue long division, lets add zeroes by putting decimal point.
Then the result of multiplying the quotient by 2 becomes the first digit of our subsequent divisor.
Now, after this, find out a number that is less than 300 that can be used for the new divisor.
6 is the number because its in tens place and we need multiplication as 300. So the nearest product is 64 x 4 = 256.
Now use next pair of zeroes. Out of that multiply 34 by 2 which gives 68.
Again repeat the previous step, which is to find out a number that is less than 4400 that can be used for the new divisor.
Then again add zeroes and repeat the process.

After this, you will find that the process is never-ending. So we have to stop the process after 3-5 repeating steps. The square root comes out to be: 
This is nearest to 3.5, 2nd option.

So we got the number 12 to find the square root. 12 is not a perfect square so we did a long division method to understand the concept and find out the root. Long division method is explained via text with a reference image. The final answer is 3.464