How can we use irrational numbers in math if we don’t know the full number?
In: 232
We do know the full number!
For example, the square root of 2 is an irrational number, but “√2” is a complete and usable description of the number.
You can add it (√2 + √2 = 2√2),
multiply (2√2 × 3√2 = 12),
divide (√2/2),
raise to a power (√2^2 = 2), or anything else!
Try for yourself!
Oh, you must mean we can’t see the end of the decimal representation of it! 1.41421356… it just keeps going and doesn’t repeat! Not a problem, just write √2.
Sometimes, an estimate is good enough. Let’s say I want to make a table big enough so that an XL pizza box (16 inches on the side) could fit on the table without hanging over the edge. Such a table requires a diameter of 16√2 inches, or roughly 16*1.4 = 22.4, let’s call it 23 inches. So, if I cut a circle out of wood that’s 23 inches wide, an XL pizza box can spin around at the center, and not a corner would hang off. Here, √2 was perfectly usable even using a “rational approximation,” like 1.4 (7/5).
Latest Answers