Question

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$\sqrt{x-2}=3$

Short answer

The required solution is $x=11$and the graph of the solution is given below:

Step-by-step solution

Step 1. Given information. 

We have:

$\sqrt{x-2}=3$

Step 2. Solve the equation algebraically.    

The equation is $\sqrt{x-2}=3$.

Square on both sides:

$$\begin{gathered} {\left(\sqrt{x-2}\right)}^2={\left(3\right)}^2 \\ x-2=9 \end{gathered}$$

Add $2$to both sides:

$$\begin{gathered} x-2+2=9+2 \\ x=11 \end{gathered}$$

Step 3. Verify the solution using a graphing utility.    

The solution of the equation is $x=11$.

Draw the graph of the equation $\sqrt{x-2}=3$using the graphing utility: