Question

solve the radical equation. check your solution(s). write
o solution\ if there is no solution. (sqrt{x - 4} = 3) (x = square)

Explanation:

Step1: Square both sides to eliminate radical

To solve the equation \(\sqrt{x - 4}=3\), we square both sides of the equation. Squaring the left side \((\sqrt{x - 4})^2\) gives \(x - 4\), and squaring the right side \(3^2\) gives \(9\). So we have the equation:
\(x - 4 = 9\)

Step2: Solve for x

To isolate \(x\), we add \(4\) to both sides of the equation \(x - 4 = 9\).
\(x-4 + 4=9 + 4\)
Simplifying both sides, we get \(x = 13\).

Step3: Check the solution

Substitute \(x = 13\) back into the original equation \(\sqrt{x - 4}\) to verify.
Left side: \(\sqrt{13 - 4}=\sqrt{9} = 3\), which is equal to the right side of the original equation. So \(x = 13\) is a valid solution.

Answer:

\(x = 13\)