Eli5: How operations with roots work.

Question

I’m about to take a college entrance exam and I just can’t make sense of it all. A friend of mine called them “spicy fractions” but I genuinely do not understand. Like, what does it mean, in a physical and earthly sense when you have something like 5[Square root of 2] (which according to this, it’s 50). What is this notation for, and what does it accomplish in a real world setting? What properties apply to them, and how do you even *get* to these types of numbers?

In: Mathematics

Answer 1

Alright so you know how 5^2 = 25 ? This is called squaring a number: multiplying it by itself. The square root is the opposite of this: square root 25 = 5.

Now, the square root of 50.

Square root(50) = square root(25 x 2) 

square root(25 x 2) = square root(25) x square root(2)

square root(25) x square root(2) = 5 x square root(2).

Happy to help if you have further questions!