Question

cphs : advanced algebra: concepts and connections - block (27.0831030)
radical equations and extraneous roots
which of the following is a radical equation?
$7\sqrt{x}=14$
$3 + x\sqrt{7}=13$
$x + \sqrt{5}=12$
$x^2 = 16$

Explanation:

To determine a radical equation, we recall that a radical equation is an equation in which the variable is under a radical (square root, cube root, etc.). Let's analyze each option:

Step 1: Analyze \( 7\sqrt{x} = 14 \)

In this equation, the variable \( x \) is under the square root (radical) symbol. So, this is a radical equation.

Step 2: Analyze \( 3 + x\sqrt{7} = 13 \)

Here, the radical \( \sqrt{7} \) is a constant (since 7 is a constant), and the variable \( x \) is not under the radical. So, this is not a radical equation.

Step 3: Analyze \( x + \sqrt{5} = 12 \)

The radical \( \sqrt{5} \) is a constant (since 5 is a constant), and the variable \( x \) is not under the radical. So, this is not a radical equation.

Step 4: Analyze \( x^2 = 16 \)

This is a quadratic equation (variable raised to the power of 2), and there is no radical with the variable. So, this is not a radical equation.

Answer:

\( 7\sqrt{x} = 14 \) is the radical equation.