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CAn someone help me with my radical equations?
There are several good websites to find help with radical equations. You tube has several good videos on radical equations that are free of charge.
What is the difference between a radical equation and a quadratic equation?
radical equations have sq roots, cube roots etc. Quadratic equations have x2.
Why do you have to check the solutions when you have to solve radical equations?
Checking your solution in the original equation is always a good idea,simply to determine whether or not you made a mistake.If your solution doesn't make the original equation true, then it's wrong.
Why do you check your answers for rational equations and radical equations?
You plug the number back into the original equation. If you have a specific example, that would help.
Why is the radical a2 b2 is not equal to a b?
Because a radical has two solutions, the positive and negative. This means that √(a2b2) has twice as many solutions as ab. ab is in fact a subset of √(a2b2).
When do you need to check for extraneous solutions?
You need to check for extraneous solutions when solving equations containing variables in denominators or within radical expressions. These solutions may arise from introducing new roots or excluded values during manipulations, which need to be verified to ensure they are valid in the original equation.
Why is it necessary to check for extraneous solutions in radical equations?
1) When solving radical equations, it is often convenient to square both sides of the equation. 2) When doing this, extraneous solutions may be introduced - the new equation may have solutions that are not solutions of the original equation. Here is a simple example (without radicals): The equation x = 5 has exactly one solution (if you replace x with 5, the equation is true, for other values, it isn't). If you square both sides, you get: x2 = 25 which also has the solution x = 5. However, it also has the extraneous solution x = -5, which is not a solution to the original equation.
In general when solving a radical equation should you first isolate the radical and then both sides?
It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.
What reasoning and explanations can be used when solving radical equations?
The basic method is the same as for other types of equations: you need to isolate the variable ("x", or whatever variable you need to solve for). In the case of radical equations, it often helps to square both sides of the equation, to get rid of the radical. You may need to rearrange the equation before squaring. It is important to note that when you do this (square both sides), the new equation may have solutions which are NOT part of the original equation. Such solutions are known as "extraneous" solutions. Here is a simple example (without radicals): x = 5 (has one solution, namely, 5) Squaring both sides: x squared = 25 (has two solutions, namely 5, and -5). To protect against this situation, make sure you check each "solution" of the modified equation against the original equation, and reject the solutions that don't satisfy it.
What happens if you are checking a solution for the radical expression and find that it makes one of the denominators in the expression equal to zero?
Then it is not a solution of the original equation. It is quite common, when solving equations involving radicals, or even when solving equations with fractions, that "extraneous" solutions are added in the converted equation - additional solutions that are not solutions of the original equation. For example, when you multiply both sides of an equation by a factor (x-1), this is valid EXCEPT for the case that x = 1. Therefore, in this example, if x = 1 is a solution of the transformed equation, it may not be a solution to the original equation.
What is a radical equation?
A radical equation is an equation that contains a variable inside a radical, such as a square root or a cube root. Solving radical equations involves isolating the radical term and then squaring both sides of the equation to eliminate the radical. It is important to check for extraneous solutions when solving radical equations.
CAn someone help me with my radical equations?
There are several good websites to find help with radical equations. You tube has several good videos on radical equations that are free of charge.
What is the difference between a radical equation and a quadratic equation?
radical equations have sq roots, cube roots etc. Quadratic equations have x2.
Do all quadratic equations have two solutions?
I may only be in 8th grade but I am absolutely positive that all quadratic equations have 2 solutions. No - They may have 0,1, or 2 answers For example, the problem x^2 + 8x +16 = 0 has only one solution -4. This is because the radical evaluates to 0 rendering the +/- sign irrelevant.
What are the steps to solving a radical equation?
Details may vary depending on the equation. Quite often, you have to square both sides of the equation, to get rid of the radical sign. It may be necessary to rearrange the equation before doing this, after doing this, or both. Squaring both sides of the equation may introduce "extraneous" roots (solutions), that is, solutions that are not part of the original equation, so you have to check each solution of the second equation, to see whether it is also a solution of the first equation.
Why do you have to check the solutions when you have to solve radical equations?
Checking your solution in the original equation is always a good idea,simply to determine whether or not you made a mistake.If your solution doesn't make the original equation true, then it's wrong.
Why do you check your answers for rational equations and radical equations?
You plug the number back into the original equation. If you have a specific example, that would help.
