Solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Square root of (5x − 3) − 3 = 0

We are given the equation:

\[
\sqrt{5x - 3} - 3 = 0
\]

### Step 1: Isolate the square root
To eliminate the square root, first isolate it on one side of the equation. Add 3 to both sides:

\[
\sqrt{5x - 3} = 3
\]

### Step 2: Square both sides
Square both sides of the equation to eliminate the square root:

\[
(\sqrt{5x - 3})^2 = 3^2
\]

This simplifies to:

\[
5x - 3 = 9
\]

### Step 3: Solve for \(x\)
Now, solve for \(x\). Add 3 to both sides:

\[
5x = 12
\]

Next, divide both sides by 5:

\[
x = \frac{12}{5}
\]

### Step 4: Check for extraneous solutions
Substitute \(x = \frac{12}{5}\) back into the original equation to check if it is a valid solution.



Solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Square root of (5x − 3) − 3 = 0

Learn how to solve the radical equation √(5x − 3) − 3 = 0 with a detailed, step-by-step solution. This problem covers key algebraic concepts such as isolating the square root, squaring both sides, and checking for extraneous solutions. Suitable for high school students in Grades 9-11.

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