Square Root of 137
2026-02-28 01:11 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-137

This is a method used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 137:


 Step 1 : Write the number 137, and draw a horizontal bar above the pair of digits from right to left.


Step 2 : Now, find the greatest number whose square is less than or equal to 1. Here, it is 1, Because 12=1 < 1.


Step 3 : Now divide 1 by 1 such that we get 1 as quotient and then multiply the divisor with the quotient, we get 1


Step 4: Subtract 1 from 1. Bring down 3 and 7 and place it beside the difference 0.


Step 5: Add 1 to same divisor, 1. We get 2.


Step 6: Now choose a number such that when placed at the end of 2, a 2-digit number will be formed. Multiply that particular number by the resultant number to get a number less than 37. Here, that number is 1. 


21×1=21<37.


Step 7: Subtract 37-21=16. Add a decimal point after the new quotient 11, again, bring down two zeroes and make 16 as 1600. Simultaneously add the unit’s place digit of 21, i.e., 1 with 21. We get here, 22. Apply Step 5 again and again until you reach 0. 

We will show two places of precision here, and so, we are left with the remainder, 16384 (refer to the picture), after some iterations and keeping the division till here, at this point 

              Step 8 : The quotient obtained is the square root. In this case, it is 11.704….