Which of the following is a radical equation?
[tex]x+\sqrt{5}=12[/tex]
[tex]x^2=16[/tex]
[tex]3+x \sqrt{7}=13[/tex]
[tex]7 \sqrt{x}=14[/tex]
Answer (2)
Radical equations contain variables under a radical symbol.
Examine each equation to identify if the variable is under a radical.
7 x = 14 is the only equation with x under a radical.
The radical equation is 7 x = 14 .
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 is inside a radical.
Checking Each Equation Let's examine each equation:
x + 5 = 12 : Here, x is not under a radical, but the constant 5 is. This is not a radical equation.
x 2 = 16 : Here, x is not under a radical. This is a quadratic equation.
3 + x 7 = 13 : Here, x is not under a radical, but the constant 7 is. This is not a radical equation.
7 x = 14 : Here, x is under a square root. This is a radical equation.
Identifying the Radical Equation Therefore, the radical equation is 7 x = 14 .
Examples
Radical equations are used in various fields, such as physics and engineering, to model phenomena involving square roots or other radicals. For example, the period of a simple pendulum is given by T = 2 π g L , where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. If you want to find the length of the pendulum needed to achieve a certain period, you would need to solve a radical equation.
The radical equation among the options is 7 x = 14 since it has the variable x under a radical. The other equations do not include a variable under a radical symbol. Therefore, the correct answer is 7 x = 14 .
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