I keep googling it and I still don’t understand what they are and their differences 😭😭
In: 18
So x³=8 what is x? You might have a few questions like can x be a set of numbers or just one? If we think about this question like we need a function that undoes the cubing or squaring there can be more answers. Like x²=4 both -2 and 2 squared is 4 so this function would have to output both -2 and 2 an an answer. That isn’t a function so we have to define what a root is. The root is always the positive.
If I ask it like this x²=4 what is x? x is -2 or 2. But if I ask sqrt(4)=x, x by definition is 2.
So now we have an idea and a solid definition about roots. The root is now a function with one parameter the kind of root you want squareroot, cuberoot…
Rational numbers are numbers you can write as a ratio of two intigers. ⅘, ⅔, ⅞… or 1, 2, 3 or -77. These are rational. Irrational numbers are numbers that cannot be expressed with a ratio between two intigers. The root is a process or now we can call it a function that sometimes outputs Irrational numbers even when you give it rational imputs. Like 2, sqrt(2) = well thats the thing. Thats the most compact form you can write it.
Roots are very misbehaved if you allow only whole numbers the outputs lead into real numbers and imaginary numbers.
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