hi this is Mario with Mario's math tutoring coming to another math video to help you boost your score in your math class improve your understanding and hopefully make learning math a lot less stressful so what we're going to talk about in this video is just an easy way to simplify radicals okay an easy method now a lot of times the way teachers teach this technique is they'll say try to divide out perfect squares like you know divide out 4 9 16 25 like divide out perfect squares so you can simplify the radical problem with this method is that sometimes students they don't have a really good grasp of their multiplication skills or even like working with really large numbers knowing like what numbers divided and evenly and they're constantly checking with your calculator so I like this method all you have to do is do a prime factorization tree you just break down the number you say well 48 that's really like 8 times 6 and 8 that's like 4 times 2 and 6 is like 3 times 2 and you just keep breaking it down until you get to just the prime numbers once you get down to the prime numbers the numbers are only divisible by one in themselves you look for a pair ok if you're taking the square root or if you're taking a cube root like this one here then you look for three of the same number if you're taking the fourth root you look for for the same number and what I usually do is I group them together so here we're taking the square root you don't see it but there's a two understood there and so we're looking for a pair meaning two of the same number it doesn't have to be the number two just two you know a pair like a pair of shoes two so we have a pair of twos a pair of 2s and a 3 left over ok we don't want to count these just the ones at the ends of the branches so 2 times 2 is 4 square root of 4 is 2 so for each group you get one of that quantity see this is 4 square root of 4 is 2 and then we have a 3 left over that stays underneath the radical so this is going to be 4 square root of 3 now if you want to check your answer you just take this number on the outside for you square it that's 16 multiplied by what's on the inside 3 and you get back the original 48 okay so let's take another look at another example the square root of 72 72 is actually now another point is that sometimes students don't even know maybe what goes into 72 you might be in that boat well if it's an even number meaning in NZ even number like zero two four six or eight you can always cut it in half you can always divide it by two so you could write this as 2 times 36 this is even you could divide it by two again this is even you could divide it by two again and then once you get down to some smaller numbers you'll know what goes in from there but you're looking for you know again a pair to the same number so we've got a pair of twos we've got a pair of threes and we have that two left over so this is going to be 3 times 2 which is 6 square root of 2 because 3 times 3 is 9 square root of 9 is 3 2 times 2 is 4 square root of 4 is 2 so 2 times 3 is the 6 and we have this 2 left over that's not a perfect square that stays underneath the square root and you got it last example we're going to do is a cube root 96 let's break this one down we've got 2 times 48 half of 48 is 24 half of 24 is 12 half of 12 is 6 and half of 6 is 3 right so we're broke it down we're taking the cube root so we're looking for 3 of the same number 2 times 2 times 2 is 8 the cube root of 8 is 2 right here we don't have enough to make another group of 3 of the same number so we're just going to work with this one cube root of 8 is 2 so you can see for each group you just get one of that group 1 of that number and then we're left with 2 times 2 times 3 which is 12 so this is 2 times the cube root of 12 and you've simplified it so I hope that helps you understand how to simplify radicals a little bit better go ahead and subscribe to the channel check out some of my past videos and I look forward to helping you with your math in the future ones I'll talk to you soon