Chapter 9 - Roots and Radicals - 9.5 - Solving Radical Equations - Problem Set 9.5 - Page 424: 12

n=16

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.