To determine which of the given equations is a radical equation, we need to identify an equation that contains a variable inside a radical, usually a square root.
The equations provided are:
1. [tex]\( x \cdot \sqrt{3} = 13 \)[/tex]
2. [tex]\( x + \sqrt{3} = 13 \)[/tex]
3. [tex]\( \sqrt{x} + 3 = 13 \)[/tex]
4. [tex]\( x + 3 = \sqrt{13} \)[/tex]
Let's examine each equation to see which one contains a variable inside a square root:
1. [tex]\( x \cdot \sqrt{3} = 13 \)[/tex]:
- Here, the variable [tex]\( x \)[/tex] is multiplied by the square root of 3. The variable is not inside the square root. Therefore, this is not a radical equation.
2. [tex]\( x + \sqrt{3} = 13 \)[/tex]:
- In this equation, the variable [tex]\( x \)[/tex] is added to the square root of 3. Again, the variable is not inside the square root. Hence, this is not a radical equation either.
3. [tex]\( \sqrt{x} + 3 = 13 \)[/tex]:
- In this expression, we have the variable [tex]\( x \)[/tex] inside the square root. This makes it a radical equation.
4. [tex]\( x + 3 = \sqrt{13} \)[/tex]:
- Here, the square root contains the constant 13, not the variable [tex]\( x \)[/tex]. Thus, the variable is not inside the square root. This is not a radical equation.
Based on the analysis, the radical equation is:
[tex]\[ \sqrt{x} + 3 = 13 \][/tex]
So, the correct answer is the third equation:
[tex]\[ \sqrt{x} + 3 = 13 \][/tex]
