The decimal expansion of √2

The square root of 2 is an irrational number, which means it cannot be expressed as a simple fraction and its decimal expansion never ends or repeats. However, it can be approximated to a decimal. Here are the steps to find the decimal expansion of √2:

1. Start by understanding that the square root of 2 is the number which, when multiplied by itself, gives the number 2.

2. Use a calculator to find the square root of 2. Most calculators have a square root function. On a scientific calculator, you would generally type "2" and then the "square root" button.

3. The calculator will give you an approximation of the square root of 2, which is about 1.41421356.

4. This is an approximation. The actual decimal expansion of √2 goes on forever without repeating.

So, the decimal expansion of √2 is approximately 1.41421356.