math.sqrt for very large numbers returns wrong value. Attached is screen shot showing my sqrt function result and math.sqrt function result.

The math module uses the float type which has a limited precision: it's 64-bit IEEE.

For better precision, you can use the decimal module which has configurable precision.

Example:
---
import decimal

decimal.getcontext().prec = 5
root = decimal.Decimal('123').sqrt()
print(root)

decimal.getcontext().prec = 50
root = decimal.Decimal('123').sqrt()
print(root)
---

Output:
---
11.091
11.090536506409417162051600102609932918463376742454
---

Said differently: the behaviour that you noticed is not a bug, but a known limitation of Python, of the Python float type to be exact.

https://docs.python.org/3/tutorial/floatingpoint.html