Write an equation of the line in slope-intercept form.

Group the digits of the number in pairs. You will start pairing from the decimal point and move away from the decimal point. E.g. for 201.64, first pair would be 2, second would be 01, and third would be 64 (see the attachment for visualizing)
Now start with the first pair, and find the number whose square is equal to or just less than the first pair. So here, since first pair is 2, that number whose square is just less than or equal to 2 is 1. Now divide 2 by 1 , and also put 1 in the quotient.
After this step, you will have 1 in quotient, and 1 in divisor with remainder of 2 - 1 = 1. Now bring down the next pair to join with the remainder. The resulting number now is 101
Now, double the number that is there in the quotient (so 1 becomes 2) and use it to determine the new divisor for 101. The new divisor will be such that when the divisor is multiplied with its unit digit then the product is just less than or equal to 101 (i.e. 2x * x <= 101). So for x = 4, 24 *4 = 96, which is less than 101. Now append this 4 in the quotient. The quotient now become 14. And subtract 96 from 101 to find the remainder. The remainder now is 5
We have now reached the decimal point in the dividend, so add a decimal point in the quotient
Now bring down the next pair to join with the remainder. The resulting number now is 564
Now, double the number that is there in the quotient (so 14 becomes 28) and use it to determine the new divisor for 564. The new divisor will be such that when the divisor is multiplied with its unit digit then the product is just less than or equal to 564 (i.e. 28x * x <= 564). So for x = 2, 282 *2 = 564. Now append this 2 in the quotient. The quotient now become 14.2. And subtract 564 from 564 to find the remainder. The remainder now is 0. Hence, we have completed the problem, and we have the square root with us
The square root is the quotient obtained: 14.2

Please refer to the attached image to see how the calculations are done