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# Simplifying square roots of fractions

## Video transcript

so we have here the square root the principal root of one two hundredths and what I want to do is simplify this when I say simplify it I really mean I want to if there's any perfect squares here that I can that I can factor out to take it out from under the radical and so I encourage you to pause the video and see see if you can do that all right 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 1 over the square root of 200 square root of 1 is just 1 over the square root of 200 and there's a couple of ways to try to simplify the square root of 200 I will I'll do it a couple of ways here square root of 200 you could realize that okay look 100 is a perfect square and it goes into 200 so this is the same thing as 2 times 100 and so the square root of 200 is the square root of 2 times the times 100 which is the same thing as the square root of 2 times the square root of 100 and we know that the square root of 100 is 10 so it's the square root of 2 times 10 or we could write this as 10 square roots of 2 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 all right let me do this in another this alternate method in a different color you could say that's the same color that I've been doing before you could say that the square root of 200 say well it's divisible by 2 so it's 2 times 100 and if 100 didn't jump out at you is a perfect square you could say well that's just going to be 2 times 50 well I could still divide 2 into that that's 2 times 25 let's see and it's 25 if that doesn't jump out at you as a perfect square you could say that we'll see that's not divisible by 2 not divisible by 3 4 but it is divisible by 5 that is 5 times 5 and to identify the perfect squares you would say alright what are there any factors where I have at least two of them well I have two times to here and I also have 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 two times two let me just from let me just write it all out so to check the common around of space so the square root give myself more space under the radical square root of two times 2 times 5 times 5 times 5 times 5 times 2 times 2 when I wrote it this order so you can see the perfect squares here well this is going to be the same thing as the square root of 2 times 2 this second method is a little bit more monotonous but hopefully it's it you see that it works this is one way to think about it and that they really they boil out of the same method we're still going to get to the same answer so square root of 2 times 2 times the square root times the square root of 5 times 5 times the square root of 5 times 5 times the square root of 2 times the square root of 2 well the square root of 2 times 2 is just going to be this is just 2 square root of 5 times 5 well that's just going to be 5 so you have 2 times 5 times the square root of 2 which is 10 times the square root of 2 equals 10 times the square root of 2 so this right over here is square root of 200 we can rewrite as 10 square roots of 2 so this is going to be equal to 1 over 10 square roots of 2 now some people don't like having a a radical in the denominator and if you wanted to get rid of that you could multiply both the numerator in the denominator by square root of 2 because notice we're just multiplying by 1 we're expressing 1 square root of 2 over square root of 2 and then what that does is we rewrite this as the square root of 2 over 10 times the square root of 2 times the square root of 2 well the square root of 2 times square root of 2 is just going to be 2 so it's going to be 10 times 2 which is 20 so it could also be written like also be written like that so hopefully you found you found that 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 these are all the same thing