Square root of 320
2026-02-28 17:21 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-320

Long Division method is 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 for non-perfect squares. To make it simple it is operated on divide, multiply, subtract, bring down and do-again.

To calculate the square root of 320:


Step 1: On the number 320.000000, draw a horizontal bar above the pair of digits from right to left.


Step 2 :Find the greatest number whose square is less than or equal to 3. Here, it is 1, Because 12=1 < 3.


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


Step 4: Subtract 1 from 3. Bring down 2 and 0 and place it beside the difference 2.


Step 5: Add 1 to the 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 220. Here, that number is 7. 


27×7=189<220. In quotient’s place, we also place that 7.


Step 7: Subtract 220-189=31.  Add a decimal point after the new quotient 17, again, bring down two zeroes and make 31 as 3100. Simultaneously add the unit’s place digit of 27, i.e., 7 with 27. We got here, 34. 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, 19456 (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 17.888….