To solve a radical equation, isolate the radical term and raise both sides to eliminate the radical. Solve the resulting equation and check for extraneous solutions.
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Solving radical equations can be tricky, but by following a few steps, the process can be simplified. The first step is to isolate the radical term by moving all other terms to the opposite side of the equation. For example, if the equation is √x + 5 = 9, subtract 5 from both sides to get √x = 4.
The next step is to raise both sides of the equation to eliminate the radical. If the radical is a square root, then square both sides. In the above example, squaring both sides gives x = 16. However, it is important to remember that when squaring both sides, extraneous solutions may arise. This means that a solution may satisfy the squared equation, but not the original equation. Therefore, it is important to check for extraneous solutions by plugging the solution back into the original equation and seeing if it works.
As Nobel Prize-winning physicist Richard Feynman once said, “If you can’t explain something in simple terms, you don’t understand it.” The following table outlines the steps for solving radical equations:
| Steps for Solving Radical Equations |
|---|
| 1. Isolate the radical term by moving all other terms to the opposite side of the equation. |
| 2. Raise both sides of the equation to eliminate the radical. |
| 3. Check for extraneous solutions by plugging the solution back into the original equation. |
Interesting facts about radical equations include that they are used in various fields such as mathematics, physics, and engineering. They are also used to solve real-world problems, such as finding the distance between two points or calculating the volume of a cone. Additionally, many types of functions can be written as radical equations, including exponential functions, logarithmic functions, and trigonometric functions.
Video related “What are the steps to solve a radical equation?”
This video explains how to solve radical equations with different examples, including equations with square roots, cube roots, fractional exponents, and two radicals and a number. The video highlights the importance of checking solutions, as squaring both sides of an equation may introduce an extraneous solution. Additionally, the importance of considering the domain of the solution is emphasized. Techniques such as moving one of the radicals and finding the correct suitable pairs of numbers to factorize difficult trinomials are also discussed. The video concludes by illustrating an example where the importance of solution verification is demonstrated.
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Solve Radical Equations
- Isolate the radical on one side of the equation.
- Raise both sides of the equation to the power of the index.
- Solve the new equation.
- Check the answer in the original equation.
How To solve Radical Equations
- 1) Isolate radical on one side of the equation
- 2) Square both sides of the equation to eliminate radical
- 3) Simplify and solve as you would any equations
Key Steps: 1) Isolate the radical symbol on one side of the equation 2) Square both sides of the equation to eliminate the radical symbol 3) Solve the equation that comes out after the squaring process 4) Check your answers with the original equation to avoid extraneous values
Follow the following four steps to solve radical equations. 1. Isolate the radical expression. 2. Square both sides of the equation: If x = y then x2 = y2. 3. Once the radical is removed, solve for the unknown.
Here are the steps we take when solving radical equations.
1) Isolate the radical expression on one side of the equation.
2) Square both sides of the equation to remove the radical symbol
3) Solve for the unknown variable
4) Check the solution in the original equation to remove any extraneous solution.
We will take the equation below as an example.
12=9+x+10
2=9+x
22=(9+x)2
4=9+x⇒x=−5
Check the solution in the original equation
12=9−5+10
12=12
Hence, x = -5 is the solution.
These topics will undoubtedly pique your attention
- Isolate the radical expression.
- Square both sides of the equation: If x = y then x2 = y2.
- Once the radical is removed, solve for the unknown.
- Check all answers.
Solving Radical Equations
To solve radical equations, follow these steps: First, isolate the radical expression on one side of the equation. For square roots, square each side of the equation to eliminate the square root. For cubic roots, after isolating, cube each side of the equation to eliminate the cubic root.
- Find the largest factor in the radicand that is a perfect power of the index. Rewrite the radicand as a product of two factors, using that factor.
- Use the product rule to rewrite the radical as the product of two radicals.
- Simplify the root of the perfect power.