Question

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

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: $\sqrt{x} + 3 = 13$: The variable $x$ is under the square root (radical), so this fits the definition of a radical equation.
• Option 2: $x + \sqrt{3} = 13$: The radical ($\sqrt{3}$) has a constant, not the variable under it. So not a radical equation.
• Option 3: $x + 3 = \sqrt{13}$: The radical ($\sqrt{13}$) has a constant, not the variable under it. So not a radical equation.
• Option 4: $x\sqrt{3} = 13$: There's no radical with the variable; it's just a coefficient with a radical. So not a radical equation.

Answer:

$\boldsymbol{\sqrt{x} + 3 = 13}$ (the first option in the top - left/top - right? Wait, looking at the layout: the first box (top right maybe? Wait the first equation shown is $\sqrt{x}+3 = 13$, so the answer is the equation $\sqrt{x}+3 = 13$ (the first rectangular box with that equation).