Square root of 193
2026-02-28 10:54 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-193

In the case of non-perfect squares, we can use long division to get a more accurate decimal place.


Step 1: Begin by pairing the digits of 193 from the right. As 193 has three numbers, consider “1” and “93” as a combination.


Step 2: Pick the largest number which, when squared, results in a number less than or equal to (√1) group. That number is 1, as 1×1=1. 


Step 3: Drag down the pair of 93 at the right of the remainder 0, and now we have our new division which is 93. 


Step 4: Now add 1, the last digit of the quotient to the divisor that is 1 so 1+1=2 and now to the right of 2, find a digit such that 2X is less than or equal to 93. When we find X, X is 3, so the new divisor is 23 for the new dividend 93.


Step 5: Now the next thing you need to do is divide 93 by 23 which will result in 3 as our quotient and give us a remainder, 93 - (23×3) = 93–69 = 24


Step 6: Drag down the pair of zeroes to the right of 24, and now we have our new remainder as 2400. 


Step 7: We need to add the last digit of the quotient to the divisor, which is 3+23=26, and need to find a digit such that 26y is less than or equal to 2400. So now together it will form a new divisor that is 268 for the new dividend of 2400. 


Step 8: 2400 is divided by 268, and we get the quotient as 8 which will give us the remainder as 2400 - (268×8) = 2400–2144 = 256


Step 9: Drag down the pair of zeroes and keep repeating the above steps till the desired decimal values. 
From the above calculations and steps, we can conclude that the square root of 191 is ±13.8