A radical equation is an equation that involves a variable under a radical symbol (such as a square root or cube root).
More detailed answer to your question
A radical equation is an equation that contains a variable within a radical, such as a square root or cube root. These equations are often more challenging to solve than standard equations, as the variable exists within the radical.
According to math expert Margaret Lial, “Radical equations are equations that have algebraic expressions with radicals in them.” This means that solving these equations often requires a series of algebraic manipulations to isolate the variable outside of the radical.
One method for solving radical equations is to isolate the radical by squaring both sides of the equation, which eliminates the radical. However, this method should be used with caution as it can introduce extraneous solutions that do not satisfy the original equation.
Fun facts about radical equations include:
- The ancient Greek mathematician Hippocrates of Chios is credited with discovering the mathematical concept of the squaring of the circle, which involves solving a radical equation.
- The study of polynomial equations with radicals led to the discovery of the Abel-Ruffini theorem, which states that there are certain polynomial equations that cannot be solved algebraically using radicals.
- Radical equations play a key role in the field of electrical engineering, particularly in circuit analysis.
Here is an example of a radical equation and its solution:
√(x + 4) = 6
To solve for x in the above equation, we must isolate the radical. First, we square both sides of the equation:
(√(x + 4))^2 = 6^2
x + 4 = 36
Next, we can solve for x by subtracting 4 from both sides:
x = 32
Therefore, x = 32 is the solution to the radical equation √(x + 4) = 6.
Table:
Example Radical Equations and Solutions
Equation | Solution
√(x + 4) = 6 | x = 32
√(2x – 1) = 3 | x = 5
3√x + 2 = 11 | x = 27/8
∛(x + 2) + 4 = 7 | x = 1
Overall, radical equations are a fascinating topic in mathematics that require careful manipulation and attention to detail in order to solve.
There are additional viewpoints
A radical equation is one in which the unknown is contained as part of the radicand of a radical expression.
A radical equation is an equation that contains one or more radicals with a variable in the radicand. The radical can be any root, such as square root, cube root, or fourth root. To solve a radical equation, one method is to raise both sides of the equation to the same power. The equation may have a condition that the radicand must be non-negative.
A radical equation is any equation that contains one or more radicals with a variable in the radicand. Following are some examples of radical equations, all of which will be solved in this section: √2x − 1 = 3 3√4×2 + 7 − 2 = 0 √x + 2 − √x = 1 The squaring property of equality states that if given real numbers a and b that
Answer: A radical equation is any equation that involves any type of radical (square root, cube root, fourth root, et cetera). Explanation: Examples of radicals are: #sqrt(46)#and #³sqrt(81)#. A radical equation is an equation that comprises one or more radicals.
A radical equation is the one that has at least one variable expression within a radical, most often the square root. The radical can be any root, maybe square root, cube root. Generally, you solve equations by isolating the variable by undoing what has been done to it.
Radical equations (also known as irrational) are equations in which the unknown value appears under a radical sign. The method for solving radical equation is raising both sides of the equation to the same power. If we have the equation $\sqrt {f (x)} = g (x)$, then the condition of that equation is always $f (x) \geq
Video answer to your question
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.
More interesting questions on the issue
Consequently, What does it mean for an equation to be a radical equation quizlet? What is a radical equation? An equation that contains at least one variable under a square, cubic, fourth etc. root.
What is an example of a radical equation?
The answer is: Example 1. Solve: √3x+1=4. Solution: We can eliminate the square root by applying the squaring property of equality.
One may also ask, How do you know if a function is radical? If a function is defined by a radical expression, we call it a radical function. The square root function is f(x)=√x f ( x ) = x . The cube root function is f(x)=3√x f ( x ) = x 3 . A radical function is a function that is defined by a radical expression.
Also Know, What is the difference between radical function and radical equation? Answer: A radical function contains a radical expression with the independent variable (usually x) in the radicand. Usually radical equations where the radical is a square root is called square root functions. The value of b tells us where the domain of the radical function begins.
Likewise, What are the steps to solve a radical equation?
In reply to that: The steps for solving radical equations involving square roots are outlined in the following example. Solve: √2x − 1 + 2 = x. Step 1: Isolate the square root. Step 2: Square both sides. Step 3: Solve the resulting equation. Step 4: Check the solutions in the original equation.
In respect to this, What is a radical equation? Response: A Radical Equation is an equation with a square root or cube root, etc. We can get rid of a square root by squaring. (Or cube roots by cubing, etc) But Warning: this can sometimes create "solutions" which don’t actually work when we put them into the original equation. So we need to Check!
Likewise, What is the index of a radical? The reply will be: The index of the radical tells the number of times you need to remove the number from inside to outside radical. Move only variables that make groups of 2 or 3 from inside to outside radicals. Simplify the expressions both inside and outside the radical by multiplying. Simplify by multiplication of all variables both inside and outside the radical.
What is the domain of a radical function?
Response: A radical function is a function that contains a square root. Radical functions are one of the few types of functions that require you to consider the domain of the function before you graph the function. The domain is the x values of a given function or relation.
Also, What are the steps to solve a radical equation?
Answer: The steps for solving radical equations involving square roots are outlined in the following example. Solve: √2x − 1 + 2 = x. Step 1: Isolate the square root. Step 2: Square both sides. Step 3: Solve the resulting equation. Step 4: Check the solutions in the original equation.
What is a radical equation? A Radical Equation is an equation with a square root or cube root, etc. We can get rid of a square root by squaring. (Or cube roots by cubing, etc) But Warning: this can sometimes create "solutions" which don’t actually work when we put them into the original equation. So we need to Check!
Consequently, What is the index of a radical? The index of the radical tells the number of times you need to remove the number from inside to outside radical. Move only variables that make groups of 2 or 3 from inside to outside radicals. Simplify the expressions both inside and outside the radical by multiplying. Simplify by multiplication of all variables both inside and outside the radical.
Besides, What is the domain of a radical function?
A radical function is a function that contains a square root. Radical functions are one of the few types of functions that require you to consider the domain of the function before you graph the function. The domain is the x values of a given function or relation.