How can we use irrational numbers in math if we don’t know the full number?

Question

How can we use irrational numbers in math if we don’t know the full number?

In: 232

Answer 1

We can use √2 because we know that √2 × √2 = 2. Sometimes we don’t even need to calculate it out in decimal; because the √2’s end up cancelling out.

We also know that √2 is the length of the hypotenuse of a right triangle whose sides have length 1, because of the Pythagorean theorem: a² + b² = c², so if a = b = 1, then c = √2.

That means that if we can measure a right angle and a side of length 1, we can measure something of √2 length without ever having to have a √2 mark on our ruler.