Python math.isqrt() Function: Usage and Examples

Find the exact integer floor of a nonnegative square root.

What You Will Learn

math.isqrt() uses integer arithmetic and does not suffer float rounding for large inputs. It is a compatibility alias for math.integer.isqrt in Python.

For floating-point results, remember that stored values are approximations. Rounding a displayed value does not change the exact value used by later calculations.

Step-by-Step Example

The example below makes the behavior visible with small input values that you can change safely.

import math
print(math.isqrt(99))

How the Example Works

The imports provide the standard-library tools used in the demonstration: math.
The print() calls make the return values or state visible so you can compare them with the explanation and check your prediction.

For the chosen input, the expression math.isqrt(99) prints 9. The result is an exact integer and never rounds up to the next root.

Expected output from the example:

Another Example: Compare the Results

Try a second input and compare it with the first. Notice whether the result changes in type, value, order, or number of items.

import math
print(math.isqrt(15), math.isqrt(16))

Expected output:

3 4

When You Would Use This

This operation can support measurements, numeric reports, simulations, or input validation. Choose integer operations when exact integer answers are required, and check floating-point rounding when displaying measured values. Validate units and input domains before using the result in a calculation.

Practice: Modify the Code

Determine how many complete square rows fit into 99 tiles.

Verify the changed output against the behavior described above, including the relevant invalid or boundary case.

For complete parameters and version details, consult the official Python documentation.

Common Beginner Mistakes

Assuming isqrt() rounds to the nearest integer or accepts negative values.
Skipping invalid or boundary inputs when adapting a numeric function to real user data.

Key Takeaways

Find the exact integer floor of a nonnegative square root.
math.isqrt() uses integer arithmetic and does not suffer float rounding for large inputs.
Apply this operation only after checking the assumptions and input conditions shown in the example.