To determine which of the given options is a radical equation, we need to check whether the variable [tex]\( x \)[/tex] is inside a radical (typically a square root). Let's evaluate each option step-by-step:
1. [tex]\( x \sqrt{3} = 13 \)[/tex]
- In this equation, the variable [tex]\( x \)[/tex] is not inside the square root. The radical [tex]\( \sqrt{3} \)[/tex] is a square root, but it doesn’t involve the variable [tex]\( x \)[/tex].
2. [tex]\( x + \sqrt{3} = 13 \)[/tex]
- Similarly, in this equation, the variable [tex]\( x \)[/tex] is not inside the square root. The term [tex]\( \sqrt{3} \)[/tex] is just a constant and does not include the variable [tex]\( x \)[/tex].
3. [tex]\( \sqrt{x} + 3 = 13 \)[/tex]
- In this equation, the variable [tex]\( x \)[/tex] is indeed inside the square root, making it a radical equation. This satisfies our condition for being a radical equation.
4. [tex]\( x + 3 = \sqrt{13} \)[/tex]
- Again, in this equation, the variable [tex]\( x \)[/tex] is not inside the square root. The term [tex]\( \sqrt{13} \)[/tex] is just a constant and does not include the variable [tex]\( x \)[/tex].
Therefore, the correct option where the variable [tex]\( x \)[/tex] is inside the square root, making it a radical equation, is:
[tex]\[ \sqrt{x} + 3 = 13 \][/tex]
So, the correct option is:
[tex]\[ \boxed{3} \][/tex]
