Question

Solve:$\sqrt{3p+3}+3=5$.

Short answer

The solution is$p=\frac{1}{3}$.

Step-by-step solution

Step 1. Given Information   

We are given the quadratic equation $\sqrt{3p+3}+3=5$and we need to solve it.

Step 2. Finding the solution  

Isolating the radical on one side of the equation:

$$\begin{gathered} \sqrt{3p+3}+3=5 \\ \Rightarrow \sqrt{3p+3}+3-3=5-3 \\ \Rightarrow \sqrt{3p+3}=2 \end{gathered}$$

Squaring both sides of the equation, we get:

$$\begin{gathered} {\left(\sqrt{3p+3}\right)}^2={\left(2\right)}^2 \\ \Rightarrow 3p+3=4 \\ \Rightarrow 3p=4-3 \\ \Rightarrow 3p=1 \\ \Rightarrow p=\frac{1}{3} \end{gathered}$$

Step 3. Checking the answer  

$$\begin{gathered} p=\frac{1}{3}, \\ \sqrt{3p+3}+3=5 \\ \Rightarrow \sqrt{3\times \frac{1}{3}+3}+3=5 \\ \Rightarrow \sqrt{1+3}+3=5 \\ \Rightarrow \sqrt{4}+3=5 \\ \Rightarrow 2+3=5 \\ \Rightarrow 5=5 \end{gathered}$$