So how do you do radical expressions, that sounds difficult doesn't it? Hi I'm Jimmy Chang, I've been teaching college mathematics for 9 years and I'm going to give you a couple of tips as to how to solve and evaluate radical expressions. Now I'm going to break it up into two cases, one involving numbers and one involving variables. Now if you know how to do them separately you should know how to do them together as well. So here's an example involving numbers. Suppose you have the square root, lets just say 18 and you want to evaluate the square root of 18. Well one quick way to do it involves knowledge of your multiplication tables. Now what you want to do is pick a couple of numbers that you know multiplied will give you 18. So one list might be 6 and 3, 9 and 2, and of course 18 and 1. Now out of these three numbers think about which pair has what's called a perfect square. Now a perfect square meaning what number when you square itself gives you that number. So for example, is the number squared going to give you 6? No, the same thing you can say for 3, no number squared gives you 3, no number squared gives you 2, but 9 is a perfect square, because 3 times 3, 3 squared gives you 9. So that is the one pair that we'll work with. Now break-up the 18 into 9 times 2 and there is a square root rule or a radical rule that lets you break up this expression as two separate ones, in other words you can re-write this as squared of 9 times the squared of 2. Now squared of 9 is obviously 3, but squared of 2, you can't break that up any further than what you already have. Now here's an example involving variables. Suppose you want to find out the cube root, of lets just say X to the 8th. Now if you know your long division figuring, this out is very straight forward. The 3 goes on the outside dividing into the exponent you see here; 3 goes in 8 how many times, 2; 2 times 3 is 6, remainder, 2. Now this 2 is the exponent that goes on the outside and this remainder 2 is the exponent that stays on the inside. In other words cube root of 8 means the cube root, the X squared goes on the outside, and this 2 is the exponent that stays on the inside. So you now have cube root of X of the 8th is equal to X squared, cube root of X squared. So I'm Jimmy, and that gives you a glimpse as how to simplify radical expressions.
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