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# Simplifying square roots

CCSS.Math:

## Video transcript

let's see if we can simplify five times the square root of 117 117 so 117 doesn't jump out at me is some type of a perfect square so let's actually take its prime factorization and see if any of those prime factorizations any of those prime factors show up more than once so it's clearly it's a it's an odd number it's clearly not divisible by two to test whether it's divisible by three we can add up all of the digits and we explain why this works in it in another place on Khan Academy but if you add up all the digits you've got a nine and nine is divisible by 3 so 117 is going to be divisible by three now let's do a little aside here and figure out what 117 divided by 3 actually is so three goes in doesn't go into one it does go into 11 3 times 3 times 3 is 9 subtract you got a remainder of 2 bring down a 7 3 times lioka 3 goes into 27 9 times 9 times 3 is 27 subtract and you're done it goes in perfectly and so this so we can factor 117 as 3 times 39 now 39 we can factor as that jumps out more at us that's divisible by 3 that's equivalent to 3 times 13 and then all of these are now prime numbers so we could say that this thing is the same as 5 times the square root the square root of 3 times 3 3 times 3 3 times 3 times 13 times 13 and this is going to be the same thing as and we know this from our exponent properties as 5 times the square root of 3 times 3 5 times the square root of 3 times 3 times the square root times the square root of 13 now what's the square root of 3 times 3 what's the square root of 9 that's the square root of 3 squared any of those well that's just going to give you 3 so this is just going to simplify to 3 so this whole thing is 5 times 3 times the square root of 13 so this part right over here would give us 15 times the square-root times the square root of 13 let's do one more example here so let's try to simplify three times the square root of 26 actually 26 in yellow like I did in the previous problem 26 well 26 is clearly an even number so it's going to be divisible by 2 we can rewrite it as 2 times 13 and then we're done 13 is a prime number we can't factor this anymore and so 26 doesn't have any perfect squares in it it's not like we can factor it out as the factor some other numbers and some perfect squares like we did here 117 is 13 times 9 it's the product of a perfect square and 13 26 isn't so we've simplified this about as much as we can we would just leave this as 3 times the square root of 26