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Simplifying square roots of fractions

Sal rewrites √(1/200) as 1/(10*√2) and as √2/20.

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  • leafers ultimate style avatar for user Drew B.
    At Sal says that sqrt(2) * sqrt(2) is 2. How does that work?
    (14 votes)
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  • aqualine ultimate style avatar for user Andrew B
    How on earth is ONE 200th equal to a 20th of the square root of 2?
    The square root of 200 is equal to a 20th of the square root of 2. Not ONE 200th.
    Please explain... I, and my calculator are both confused.
    (7 votes)
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    • mr pink red style avatar for user andrewp18
      I'm not sure what you mean.
      1/200 ≠ √2/20
      I know this immediately because the LHS is rational and the RHS is irrational so they cannot be equivalent. What makes you think that it was implied that they were equivalent?
      (4 votes)
  • stelly orange style avatar for user Megane Thomas
    How does the square root of 2 times the square root of 2 equal 2?
    (4 votes)
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  • blobby green style avatar for user samantha  checca
    im lost on how you get 10 if 10 times 10 is 100 not 200 thats where i got lost
    (3 votes)
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  • blobby green style avatar for user Matthew  Carson
    Can someone explain why the two in purple is separated from the other twos?
    (2 votes)
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    • stelly blue style avatar for user Kim Seidel
      200 factors into 2*2*2*5*5
      When simplifying a square root, you need numbers that are squared to bring a value outside the radical. Notice, Sal pairs up the factors into (2*2)(5*5)(2). He can take the square root of (2*2), it becomes 2. He can take the square root of (5*5), it becomes 5. He can't take the square root of 2 (this is the purple 2) because there is only one 2. So, it stays in the radical.
      Hope this helps.
      (2 votes)
  • aqualine ultimate style avatar for user Max
    I understand square roots a lot better than most people in my class, but I'm stumped on how to simplify square roots this video made me a little more confused, can someone help break it down for me?
    (2 votes)
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    • piceratops ultimate style avatar for user ChrisTry162
      Just prime factorize and find any perfect squares in the number. Then find the root of those perfect square and put that outside of the square root! I recommend making sure you are familiar with these terms as sal uses it alot in his later videos.
      (2 votes)
  • duskpin tree style avatar for user AwesomeK
    How do you make a square root into a fraction? Like 2√7?
    (2 votes)
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  • starky tree style avatar for user Rylie
    what do you do when it looks like this...7^3/^5?
    (2 votes)
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    • leaf orange style avatar for user vrushank
      This is kind of a wrong statement that you are giving , the fifth power you are raising must have a base but here it does not have any .
      This statement is like 7 raised to the power 3 divided by 'something' raised to the power 5 , but what is that 'something' , thus you are giving an incomplete statement .
      (1 vote)
  • piceratops seedling style avatar for user Jared Michael Loveless
    Here's what I did and I'm not sure where I went wrong
    √1/200

    =√1/(10*10*2)
    =(1/10)*(√1/2)

    or 1/(10√12)

    Where did I go wrong? Or how is this not a right answer?
    (1 vote)
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    • stelly blue style avatar for user Kim Seidel
      Here's how I would do it.
      Split the fraction into 2 radicals.
      √(1/200) = √(1)/√(200)
      Simplify both square roots.
      √(1) = 1
      √(200) = √(10*10*2) = 10√(2)
      So, your fraction becomes: 1/[10√(2)]
      Next, a simplified radical will have no radicals in the denominator. So you need to rationalize the denominator.
      1/[10√(2)]
      = 1/[10√(2)] * √(2)/√(2)
      = √(2)/[10√(4)]
      = √(2)/[10*2]
      = √(2)/20

      Hope this helps.
      (3 votes)
  • winston default style avatar for user Nicholas Young
    What would you do if you have a fraction?
    (1 vote)
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    • leafers ultimate style avatar for user Drew B.
      I will restate the video. Example: sqrt(1/200) which is equal to sqrt(1) / sqrt(200) the sqrt of 1 is 1 so 1/sqrt(200) the sqrt(200) = sqrt(2) * sqrt(100) further simplifying sqrt(100) is 10 so sqrt(2)*10 equals the sqrt(200) so we reinsert the simplified version of sqrt(200) which will end up as 1/sqrt(2)*10 which is the answer. The video also explains sqrt in the denominator so that will help more.
      (3 votes)

Video transcript

- [Voiceover] So we have here the square root, the principal root, of one two-hundredth. And what I want to do is simplify this. When I say "simplify it" I really mean, if there's any perfect squares here that I can factor out to take it out from under the radical. And so I encourage you to pause the video and see if you can do that. Alright so there's a couple of ways that you could approach this. One way is to say, Well this is going to be the same thing as the square root of one over the square root of 200. The square root of one is just one over the square root of 200. And there's a couple of ways to try to simplify the square root of 200. I'll do it a couple of ways here. Square root of 200. You could realize that, OK, look 100 is a perfect square. And it goes into 200. So this is the same thing as two times 100. And so the square root of 200 is the square root of two times 100, which is the same thing as the square root of two times the square root of 100. And we know that the square root of 100 is 10. So it's the square root of two times 10 or we could write this as 10 square roots of two. That's one way to approach it. But if it didn't jump out at you immediately that you have this large perfect square that is a factor of 200, you could just start with small numbers. You could say, alright, let me do this alternate method in a different color. You could say, ah it's the same color that I've been doing before. (laughing) You could say that the square root of 200, say Well it's divisible by two. So it's two times 100. And if 100 didn't jump out at you as a perfect square, you could say, Well that's just going to be two times 50. Well I can still divide two into that. That's two times 25. Let's see, and 25, if that doesn't jump out at you as a perfect square, you could say that that's not divisible by two, not divisible by three, four, but it is divisible by five. That is five times five. And to identify the perfect squares you would say, Alright, are there any factors where I have at least two of them? Well I have two times two here. And I also have five times five here. So I can rewrite the square root of 200 as being equal to the square root of two times two. Let me just write it all out. Actually I think I'm going to run out of space. So the square root, give myself more space under the radical, square root of two times two times five times five times two. And I wrote it in this order so you can see the perfect squares here. Well this is going to be the same thing as the square root of two times two. This second method is a little bit more monotonous, but hopefully you see that it works, (laughing) I guess is one way to think about it. And they really, they boil down to the same method. We're still going to get to the same answer. So square root of two times two times the square root times the square root of five times five, times the square root of two. Well the square root of two times two is just going to be, this is just two. Square root of five times five, well that's just going to be five. So you have two times five times the square root of two, which is 10 times the square root of two. So this right over here, square root of 200, we can rewrite as 10 square roots of two. So this is going to be equal to one over 10 square roots of two. Now some people don't like having a radical in the denominator and if you wanted to get rid of that, you could multiply both the numerator and the denominator by the square root of two. 'Cause notice we're just multiplying by one, we're expressing one as square root of two over square root of two, and then what that does is we rewrite this as the square root of two over 10 times the square root of two times the square root of two. Well the square root of two times the square root of two is just going to be two. So it's going to be 10 times two which is 20. So it could also be written like that. So hopefully you found that helpful. In fact, even this one, you could write if you want to visualize it slightly differently, you could view it as one twentieth times the square root of two. So these are all the same thing.