How To Solve Radical Equations
How To Solve Radical Equations
In this VideoJug, clip Doctor Shah presents a simple step-by-step guide to solving radical equations. Follow his instructions and say goodbye to all of your math problems.
Hi, I'm Doctor Shah. I was the National Lecture Competition winner in 1989, and I'm the maths master at Mathschool. Now, ready for a new way of doing maths? Now, radical equation is one where X is inside the square root.
So, this first example here would not count as a radical equation because it's only got a four inside the square root, there is no X inside the square root, so that's not a radical equation. This one here is a radical equation; X is quite clearly inside the square root, so that's one that would count as a radical equation. That again would be a radical equation; X is inside the square root.
This one wouldn't be a radical equation; X isn't inside the square root, it's just a square root of three. So that's not a radical equation. This is a radical equation, and this again is a radical equation.
So, let's have a go at solving a couple of them, and we'll start with this one. The trick with solving radical equations is to start off by getting the square root term on its own on one side. So, if we're solving this equation, we don't have any problems because the square root term is on its own on one side already.
So the first thing I'm going to do is to get rid of the square root. Opposite to square root is to square. So I'm going to square both sides.
So, the square will cancel out the square root, and on this side I'm just left with X plus one, and on this side three squared is nine. And now all I need to do is minus one on both sides to solve my equation. So that's solved.
Now, when you're solving a radical equation it's very important to check your answer works back in the original equation, because the step that we have done here, squaring, introduces false solutions. Well, it's easy for you to eradicate the false solutions simply by putting them back in the original equation. So this eight, I'm going to put it back in the original equation.
Eight plus one is nine, square root to it is three which does equal three. So now I know that this is checked, so I can burn checked next to that. Okay, so we've done that one.
Let's have a go at that one, slightly more complicated example. First thing, as before, is to get the square root term on its own on one side, so that means that I need to get rid of this six here and so I'm going to minus six from both sides, and on this side, that gives me X minus six and on this side is the square root term on its own, the square root X on its own. Now I want to square both sides, the rule for squaring an equation is you must first put brackets around each side, especially if there's a plus or minus sign and separate terms, then you must put a brackets around it, and then square it.
So the square cancels out the square root on that side so I get X here, and here I get X minus six squared. Now go back to my standard rules for solving equations which is get rid of fractions, they don't have any fractions, multiply out brackets. Well, to multiply the X minus six squared I first write in X minus six times X minus six, and then I multiply out those using the four arrows that you know to use when you're multiplying out two sets of brackets.
So that gives me X squared, that's that one, this one is minus six X, this one is another minus six X, and this is plus thirty-six, and on the other side, it's equal to X. Just rub that out. And then, simplifying as I go along, that minus six X and another minus six X ad up to minus twelve X.
Okay, X squared minus twelve X plus thirty six equals X. And now, I want to collect all the terms to one side, so I'm going to minus this X. And that gives me X squared, minus thirteen X, plus thirty-six is zero.
So, I have my quadratic equal to zero now, and I want to try to factorize that quadratic. To get X squared, I'm going to put an X in the front of each of the brackets. To get thirty six, well, I could do six times six or I could do nine times four, I'm going to try nine times four but I know, actually, tha