11 12 13 14 15 16 17 18 19 Which of the following is a radical equation? \( x+\sqrt{5}=12 \) \( x^{2}=16 \) \( 3+x \sqrt{7}=13 \)

A **radical equation** is one in which the variable appears inside a radical (such as a square root, cube root, etc.). Let's examine each of the provided equations: 1. **\( x + \sqrt{5} = 12 \)** - Here, \( x \) is **not** inside a radical. The equation involves adding a constant radical (\( \sqrt{5} \)) to the variable \( x \), but the variable itself is not under the radical sign. 2. **\( x^{2} = 16 \)** - This is a **quadratic equation**, not a radical equation. The variable \( x \) is raised to a power, but it is not inside a radical. 3. **\( 3 + x \sqrt{7} = 13 \)** - In this equation, \( x \) is multiplied by \( \sqrt{7} \), but again, \( x \) is **not** inside the radical. The radical is applied only to the constant \( 7 \), not to the variable \( x \). **Conclusion:** None of the provided equations are radical equations because the variable does not appear inside a radical. A classic example of a radical equation would be something like \( \sqrt{x} + 2 = 5 \), where \( x \) is directly under the square root. **Answer:** None of the given equations qualify as a radical equation because the variable does not appear inside a radical.