Simplifying Square Roots | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to simplify square roots and we have four examples that we're going to go through together in order to get this down so let's jump into number one where we have the square root of 20. now 20 is not a perfect square so we're not going to get a nice and clean cut whole number answer so we need to simplify we can do this by looking for factors of 20 that are perfect squares and then find their square roots for example we know that 4 times 5 equals 20. 4 and 5 are factors of 20 they go into 20 so to speak 4 is a perfect square so let's do this in order to simplify the square root of 20 equals the square root of 4 times 5. now the multiplication or product property of square roots lets us split this meaning we can do this the square root of 4 times the square root of 5. that's equivalent to the square root of 20. it's equal we're not changing the value of the problem at all now we can take the square root of our perfect square 4 and we end up with well the square root of 4 is 2 bring down our square root of 5 because we cannot simplify that any further so our simplified answer is 2 times the square root of 5 or 2 square root 5. let's try another one and move on to number 2 where we have the square root of 32 so we need to think are there any factors of 32 that are perfect square so any numbers that can go into 32 so to speak that are perfect squares if so we can simplify if not it's already in simplest form well we know that 16 times 2 equals 32 and 16 is a perfect square so we can simplify the square root of 32 equals the square root of sixteen times two let's split this so we have the square root of sixteen times the square root of two sixteen is a perfect square so the square root of 16 is 4 so we end up with 4 times the square root of 2 or 4 square root 2 or you can even say 4 root 2. now 2 cannot be simplified any further so this is our final answer as far as simplifying the square root of 32. now i do want to mention we can take another path to get to that same answer for number two i'm going to try to squeeze it in to the left here we know that 4 times 8 also equals 32 and 4 is a perfect square so this is the other path we can take and i'm going to start by splitting these just to make sure i have enough room so we have the square root of four times the square root of eight the square root of four is two let's bring down our square root of eight now we can continue to simplify we're not done yet because we have a perfect square within eight as far as factors go because four times two equals eight and four is a perfect square so again we can continue to simplify so we have 2 times the square root of 4 times the square root of 2. so the square root of 4 again is 2 so we end up with 2 times 2 times the square root of 2. now the square root of 2 is simplified so we can't break that down any further but we can multiply our two times two so two times two gives us four and then we have the square root of two so same exact answer but a different path and that's okay both of those paths are correct so keep that in mind there may be different paths as far as simplifying a square root just always remember to check if you can simplify further let's move on to number three and try another one where we have the square root of 45 so think any factors that are perfect squares yes 9 and 5 are factors of 45 9 times 5 equals 45 and 9 is a perfect square so the square root of 45 equals the square root of 9 times 5. let's split this so square root of 9 times the square root of five so the square root of nine is three bring down our square root of five that cannot be simplified any further so we have three times the square root of 5 or 3 square root 5 or 3 root 5 lastly number 4 we have the square root of 75 so any factors that are perfect squares well 25 and 3 are factors of 75 25 times 3 equals 75 and 25 is a perfect square so the square root of 75 equals the square root of 25 times 3. let's split so we get the square root of 25 times the square root of 3. now the square root of 25 is 5 so we have 5 and then the square root of 3 is in simplest form so we can't break that down any further and this is our final simplified answer now i do want to mention that we always put the number before the square root symbol as you can see in all four of our final simplified answers so for example if we were to put the three first so the square root of 3 times the square root of 25 and get the square root of 3 times 5 you would want to rearrange this so you have the number first and put the square root second so you can see that we have the number then the square root so that's common practice and that's how you would want to leave your answers so there you have it there's how you simplify square roots now i would suggest really knowing the first 12 perfect squares this is going to help a lot as far as square roots go and simplifying them i have a pinned comment below with the first 12 so if you need some help with those check that out i also have some other square root videos down in the description i hope that helped thanks so much for watching until next time peace