I know it like “this multiplyed by itself has to equal 2” but does that mean when simplyfied or what?
In: Mathematics
The square root of X is the side length of a square whose area is X. If you want to make a square that covers an area of 2 units^(2), then you must make its sides sqrt(2) units long.
It simply refers to another number or quantity. Like 1, 2 or 105. Just another number. There is nothing “special” about it, in general, other than the fact that the value of the square root of 2 multiplied by itself equals 2. Sort of like 2 * 3 = 6. 2, 3 and 6 are just numbers that happen to have that relationship.
Historically speaking, sqrt(2) is significant in that it is probably the first proven irrational number. An irrational number is one which cannot be written down as an integer fraction.
When you square a number you multiply it by itself. A square root is the reverse of that, so by looking for the square root you will find out, for any given number, which two numbers need to be multiplied together to make that first number.
>I know it like “this multiplyed by itself has to equal 2” but does that mean when simplyfied or what?
I’m pretty sure you’ve got the simplest version there already. You can twist and turn it around a little bit, sometimes that helps with making it click?
If x^2 equals y, then x is the square root of y.
There isn’t really much else to it. It is just exactly that. Two of the same number multiplied together to get the square. Some square roots are rational (have an ending to the number) and some are irrational (number goes on forever). So the square root of 4 is 2. That’s a rational number. The square root of 2 is 1.41421356237309504880168872420969807856967187537…… There is no simplifying because that would change the number and therefore not be the square root.
Okay so, imagine you have a tray one inch deep, and it’s one inch wide and one inch long. And you want to fill it all the way up with water.
Now, you ask yourself “how much bigger does this tray need to be, so that it’s still one inch deep, and still square, and holds exactly twice as much water?”
The answer is the “square root of two”.
You can also ask “how much bigger does that first tray need to be, to hold FIVE times as much water at one inch deep?” And the answer is the “square root of five”
Its called the “square root” because it’s the root (side) of a square.
If instead of saying “a square, one inch deep”, you said “how big of a CUBE” would you need to hold twice as much water, the answer would be the CUBE root of two.
See how that works?
That’s it, we defined it that way.
To square something means to multiply it by itself. But if we have the result (the square of something) of that and we want to go back? Well we need to find the “root of that square.” We called it that, nothing more, nothing less.
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