To determine which of the given equations is a radical equation, we need to identify if any variables are under a radical (like a square root). Let's analyze each option step-by-step:
1. [tex]\( x + \sqrt{5} = 12 \)[/tex]
- In this equation, [tex]\( \sqrt{5} \)[/tex] is a constant and not a variable. The variable [tex]\( x \)[/tex] is not under a radical. Therefore, this is not a radical equation.
2. [tex]\( x^2 = 16 \)[/tex]
- This is a polynomial equation (specifically a quadratic equation). The variable [tex]\( x \)[/tex] is not under a radical. Therefore, this is not a radical equation.
3. [tex]\( 3 + x \sqrt{7} = 13 \)[/tex]
- Here, [tex]\( x \)[/tex] is multiplied by the constant [tex]\( \sqrt{7} \)[/tex], but the variable [tex]\( x \)[/tex] itself is not under the radical. Therefore, this is not a radical equation.
4. [tex]\( 7 \sqrt{x} = 14 \)[/tex]
- In this equation, [tex]\( x \)[/tex] is under a square root, which makes it a radical equation.
Based on this analysis, the correct choice is the fourth equation:
[tex]\[ 7 \sqrt{x} = 14 \][/tex]
Thus, the equation [tex]\( 7 \sqrt{x} = 14 \)[/tex] is a radical equation.
