OK, i know the answer, but i don't know how they got there (or the reasoning). Here's the question: The surface area of a cube is 384 cm^2. Find the length of one edge. I saw this in class, but I didn't follow it very well. All that was on the blackboard said:
6x^2=384
divide both sides by six
x^2=64
√x^2=√64
x=8
Now, I get that if a cube has six faces, and I let one face =x, that I will get 6x. But how do I get 6x^2 out of that? What is the reasoning behind the square symbol?
6x^2=384
divide both sides by six
x^2=64
√x^2=√64
x=8
Now, I get that if a cube has six faces, and I let one face =x, that I will get 6x. But how do I get 6x^2 out of that? What is the reasoning behind the square symbol?
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The area of a square of side x is:
x * x = x² (by definition of x²)
Since there are 6 sides to the cube, there are six x²'s:
6x² = 384
--> divideby 6
x² = 64
--> take the square root
x = ±√64 = ±8
x = 8 or -8
But a negative length doesn't make sense, even though mathematically x = -8 solves the equation, we reason that this is not a physical answer, so we just use +8:
x = +8
x * x = x² (by definition of x²)
Since there are 6 sides to the cube, there are six x²'s:
6x² = 384
--> divideby 6
x² = 64
--> take the square root
x = ±√64 = ±8
x = 8 or -8
But a negative length doesn't make sense, even though mathematically x = -8 solves the equation, we reason that this is not a physical answer, so we just use +8:
x = +8