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Subtracting functions

Given that f(x)=2x√5-4 and g(x)=x^2+2x√5-1, Sal finds (g-f)(x). Created by Sal Khan and Monterey Institute for Technology and Education.

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  • female robot ada style avatar for user Emma
    What does "the principle square root" mean? Sal wrote it normally as sqrt of 5, but I'm not sure what the "principle" means here, since I have always heard square roots read aloud as "square root of 5" or whatever number you're taking the square root of. Please help! Thank you.
    (19 votes)
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  • leaf green style avatar for user samuel kates
    at Sal talks about the principle square root of 5. What is a principle root? Is there a vid on it.
    (2 votes)
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  • duskpin ultimate style avatar for user Radhika Kattula
    At and various other times in the video, Sal says "principal square root." I understand the the principal square is the positive square root, but how does Sal know to read it as principal square root and not just square root? The signs are the same. Is it because we can assume that it is a function so it has to be the principal square root because otherwise it would just be a relation?
    (2 votes)
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    • marcimus pink style avatar for user Tyler
      The symbol in the video, "√", means "principle square root". It does not mean square root. Square root is written with a "plus or minus" symbol in front, so it looks like this: "±√"

      So, for instance, if we used the number "25", they would look like this
      √25 = 5 (principle square root)
      ±√25 = ±5 (square root)

      Unless you write the "plus or minus" symbol, it is always just the principle square root, not the square root. So that's how you can tell the difference. I hope this helps.
      (10 votes)
  • blobby green style avatar for user TejVnair
    At , Sal refers to the square root 5 as the principle square root of 5. Why is this?
    (2 votes)
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    • mr pants teal style avatar for user VincentTheFrugal
      A square root generally has two answers. A positive answer and a negative answer.

      A square root is asking, "what number, times itself, gives me this number?" So the square root of 25 is asking, "What number, times itself, gives me 25?". Well... 5*5 gives me 25. However, -5 * -5 also gives me 25. Both are valid answers for the square root of 25.

      In general, most of the time, you want a positive number as your answer to a square root. The positive possible answer is also known as the "principal square root". So the principal square root of 25 is 5.

      Sal just wanted to make it clear that he is using the positive possible answer, and not the negative possible answer to the square root of 5
      (4 votes)
  • leafers seed style avatar for user charlotte lehmann
    i didnt understand any of it...'
    (3 votes)
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  • blobby green style avatar for user 1005025
    The principle root of a number is just the positive square root. Each number has 2 square roots.
    (3 votes)
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  • aqualine sapling style avatar for user LittleMissAuthor1221
    I don't get it. The video won't play for me. :(
    (2 votes)
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  • piceratops tree style avatar for user jhake
    I'm confuse with the "removing the pharanthesis" part:

    On the video, if we're going to substitute g(x)-f(x) with its definition, it will become:
    (x^2+2x√5-1) - (2x√5-4). To get rid of the parenthesis, we have to multiply an imaginary -1 to the exprission, 2x√5-4. So, -1(2x√5) = -2x√5 and -1(-4) = 4, right? But why does the video say that -1(-4) = 5?
    (2 votes)
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  • orange juice squid orange style avatar for user sy258288
    so I'm 12, and I'm new to this, so do not judge me just help me, but for some reason, this is what I did:

    (x^2+2*√5-1)-(2x√5-4)
    (x^2+2*0-1)-(2x*0-4)
    (x^2-1)-(-4)
    (x^2-5)
    but the answer was x^2-3 what did I do wrong.
    (2 votes)
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    • stelly blue style avatar for user Kim Seidel
      First, you changed the expression. It should be:
      (x^2+2x√5-1)-(2x√5-4)

      Next - Where did you get the 0's from in your 2nd line? You can't change √5 into 0. They are not equal.

      The correct way to work the problem is to distribute the minus sign that is in front of the 2nd set of parentheses. This minus is the same as -1 just like "-x" is the same as "-1x". Distributing the minus or -1 results in changing the signs of the terms inside the parentheses:
      (x^2+2x√5-1)-1(2x√5-4) = x^2+2x√5-1-2x√5+4
      Then, you combine like terms:
      x^2+2x√5-1-2x√5+4 = x^2+(2x√5-2x√5)+(-1+4)
      = x^2+3

      You never applied the minus sign to the -4. Instead, you treated: "-(-4)" as just "-4".

      Hope this helps.
      (2 votes)
  • duskpin ultimate style avatar for user Josiah Terribili
    What does Sal mean by "f of x"?
    (2 votes)
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Video transcript

- [Instructor] We're told that f of x is equal to two x times the square root of five minus four. And we're also told that g of x is equal to x squared plus two x times the square root of five minus one. And they want us to find g minus f of x. So pause this video, and see if you can work through that on your own. So the key here is to just realize what this notation means. G minus f of x is the same thing as g of x minus f of x. And so, again, if this was helpful to you, once again I encourage you to pause the video. All right, now let's work through this again. So this is going, or, I guess the first time, but now that we know that this is equal to g of x minus f of x. So what is g of x? Well, that's the same thing as x squared plus two x times the square root of five minus one. And what is f of x? Well, it's going to be two x times the square root of five minus four. And we are subtracting f of x from g of x. So let's subtract, this is f of x, from g of x. And so now it's just going to be a little bit of algebraic simplification. So this is going to be equal to, this is equal to x squared plus two x times the square root of five minus one. And now we just have to distribute this negative sign. So negative one times two x times the square root of five is, we're gonna have minus two x times the square root of five. And then the negative of negative four is positive four. Now let's see if we can simplify this some. So this is going to be equal to, we only have one x squared term, so that's that one there. So we have x squared. Now let's see, we have two x times the square root of five. And then we have another, oh, and then we subtract two x times the square root of five. So these two cancel out with each other. So those cancel out. And then we have minus one plus four. So if we have negative one and then we add four to it, we're going to have positive three. So if we just fact, if we take this and this into consideration, four minus one is going to be equal to three, and we're done. That's what g minus f of x is equal to, x squared plus three.