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Which of the following is a radical equation?

A. [tex]\(x \sqrt{3} = 13\)[/tex]
B. [tex]\(x + \sqrt{3} = 13\)[/tex]
C. [tex]\(\sqrt{x} + 3 = 13\)[/tex]
D. [tex]\(x + 3 = \sqrt{13}\)[/tex]


Sagot :

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]