Question

which of the following is a radical equation?
○ $x\sqrt{3} = 13$
○ $x + \sqrt{3} = 13$
○ $\sqrt{x} + 3 = 13$
○ $x + 3 = \sqrt{13}$

Explanation:

Step1: Recall radical equation definition

A radical equation is an equation where the variable is under a radical (square root, cube root, etc.).

Step2: Analyze each option

• Option 1: \( x\sqrt{3} = 13 \) – The radical (\(\sqrt{3}\)) is a constant, variable \( x \) is not under radical.
• Option 2: \( x + \sqrt{3} = 13 \) – Radical is a constant, \( x \) is not under radical.
• Option 3: \( \sqrt{x} + 3 = 13 \) – Variable \( x \) is under the square root (radical).
• Option 4: \( x + 3 = \sqrt{13} \) – Radical is a constant (\(\sqrt{13}\)), \( x \) is not under radical.

Answer:

\(\boldsymbol{\sqrt{x} + 3 = 13}\) (the third option)