Square Root of 13
2026-02-28 19:04 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-13


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 13:


Step 1 : Write the number 13, 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 13. Here, it is 3, Because 32=9 < 13.


Step 3 : Now divide 13 by 3, such that we get 3 as quotient and then multiply the divisor with the quotient, we get 9.


Step 4: Add a decimal point after the quotient 3, and bring down two zeroes and place it beside the difference 4 to make it 400.


Step 5: Add 3 to same divisor, 3. We get 6.


Step 6: Now choose a number such that when placed at the end of 6, a 2-digit number will be formed. Multiply that particular number by the resultant number to get a number less than 400. Here, that number is 6. 


66×6=396<400.


Step 7: Subtract 400-396=4. Again, bring down two zeroes and make 4 as 400. Simultaneously add the unit’s place digit of 66, i.e., 6 with 66. We get here, 72. 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, 3975 (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 3.605….