Simplifying Radicals Easy Method

Hi, this is Mario with Mario's Math Tutoring, coming to you with 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. The 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 divide unevenly, and they're constantly checking with their 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 that are only divisible by 1 in themselves, you look for a pair, okay, if you're taking the square root. Or if you're taking a cube root like this one here, then you would look for 3 of the same number. If you're taking the fourth root, you look for 4 of 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 2 understood there. And so we're looking for a pair, meaning 2 of the same number. It doesn't have to be the number 2, just a pair, like a pair of shoes, 2. So we have a pair of 2s, a pair of 2s, and a 3 left over. Okay, 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, 4. You square it, that's 16, multiply 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 it ends in an even number like 0, 2, 4, 6, or 8, you can always cut it in half. You can always divide it by 2. So you could write this as 2 times 36. This is even. You can divide it by 2 again. This is even. You can divide it by 2 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, two of the same numbers. So we've got a pair of 2's, we've got a pair of 3's, and we have that 2 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 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, one 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.