The approximate value of the square root of 3,170 is around 56.35 which is 53 to the nearest integer.
Start with an initial guess. Let's choose 55.
55 squared is 3,025.
Increase the guess:
56 squared is 3,136.
Since 3,170 is between 56 squared and 57 squared, refine the guess:
56.5 squared is 3,202.25 (Too high).
56.3 squared is 3,162.09 (Too low).
56.4 squared is 3,181.36 (Too high).
The value is between 56.3 and 56.4, so try a value closer to 56.3:
56.35 squared is 3,172.3225 (Getting closer).
Therefore, the approximate value of the square root of 3,170 is around 56.35.