Many physical laws, particularly those dealing with forces or electromagnetic have an inverse square relationship. So, if you want to know how far you need to be before a light seems half as bright, the answer is to the distance of sqrt(2) times.
The formula for all harmonic motion - vibrations - including electromagnetic waves such as light and electricity involve pi.
The decay rate for radioactive nuclei, population growth for bacteria etc involve Euler's constant, e.
Basically, you would not get anywhere in science without Irrational Numbers.
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The sum of a rational and irrational number must be an irrational number.
rational * irrational = irrational.
No, 3.56 is not an irrational number. 3.56 is rational.
-Pi is irrational, because it does not terminate or repeat. Whenever you multiply an irrational number by a rational number (-1), the result is an irrational number.
Any irrational number, when multiplied by 0.5 will give an irrational number.