Question

which of the following is a radical equation?
$7\sqrt{x}=14$
$3 + x\sqrt{7}=13$
$x + \sqrt{5}=12$
$x^2=16$

Explanation:

Step1: Define Radical Equation

A radical equation is an equation in which the variable is under a radical (square root, cube root, etc.).

Step2: Analyze Each Option

• For \( 7\sqrt{x} = 14 \): The variable \( x \) is under the square root (radical) sign. So this is a radical equation.
• For \( x^{2}=16 \): This is a quadratic equation (variable with exponent 2), no radical with variable.
• For \( 3 + x\sqrt{7}=13 \): The radical here is \( \sqrt{7} \) (constant under radical), variable \( x \) is not under radical.
• For \( x+\sqrt{5}=12 \): The radical \( \sqrt{5} \) is a constant (radical with constant), variable \( x \) is not under radical.

Answer:

\( 7\sqrt{x} = 14 \)