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
How you do it:
You’re supposed to factor the number. For example, 6 = 2*3 and 15 = 3*5. When you’re asked to take the square root of 50, but you realize there’s no whole number answer, instead you can factor 50 into 5*5*2. Then you can break sqrt(50) into sqrt(5*5) * sqrt(2), or 5 * sqrt(2).
What is this notation for?
It’s the way to write an answer in its simplest form.
As a real-world problem, let’s say you have a right triangle and the two smaller sides are length 5. What is the length of the hypotenuse?
The pythagorean theorem says that a^2 + b^2 = c^2. Since the two sides are 5 and 5, square those and you get 25 and 25, so the hypotenuse squared is 50. So to get the hypotenuse you need the square root of 50.
However, just like when we write fractions we think it’s better to write 2/3 instead of 4/6, when writing answers involving square roots we think it’s better to write 5 sqrt(2) instead of sqrt(50).
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