#### Answer

n=16

#### Work Step by Step

Recall, in order to cancel out a square root, we square both sides of the equation. Thus, we square both sides of the equation to obtain that 3n+1=49. We subtract by one on both sides and then divide both sides of the equation by 3 to isolate n and obtain: n=16.
We now must check our solution:
$\sqrt{3(16)+1} = 7 \\\\\ \sqrt {49}=7 \\\\ 7=7$
This is true, so n=16.