Which of the following is a radical equation?
[tex]x \sqrt{3}=13[/tex]
[tex]x+\sqrt{3}=13[/tex]
[tex]\sqrt{x}+3=13[/tex]
[tex]x+3=\sqrt{13}[/tex]
Answer (2)
A radical equation contains a variable under a radical symbol.
Examine each equation to identify if x is under a radical.
x + 3 = 13 is the only equation with x under a radical.
Therefore, the radical equation is x + 3 = 13 .
Explanation
Understanding Radical Equations A radical equation is an equation where the variable is under a radical symbol (like a square root, cube root, etc.). We need to check each equation to see if the variable x is inside a radical.
Checking Each Equation Let's look at each equation:
x 3 = 13 : Here, x is multiplied by 3 , but x itself is not under a radical.
x + 3 = 13 : Again, x is not under a radical; it's being added to 3 .
x + 3 = 13 : In this equation, x is under a square root, so this is a radical equation.
x + 3 = 13 : Here, the constant 13 is under the square root, but x is not.
Identifying the Radical Equation Therefore, the radical equation among the given options is x + 3 = 13 .
Examples
Radical equations are useful in many real-world applications, such as calculating the period of a pendulum or determining the velocity of an object in physics. For example, the period T of a simple pendulum can be calculated using the formula T = 2 π g L , where L is the length of the pendulum and g is the acceleration due to gravity. Solving for L or g would involve working with a radical equation. Understanding how to solve these equations allows us to make accurate predictions and measurements in various scientific and engineering contexts.
The radical equation among the options provided is x + 3 = 13 because it is the only equation with x under a radical symbol. The other equations do not have x beneath a radical. Therefore, the answer is x + 3 = 13 .
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