Chapter 6 - Radical Functions and Rational Exponents - 6-5 Solving Square Root and Other Radical Equations - Practice and Problem-Solving Exercises - Page 395: 12

$x = 15$

$\sqrt {x+1} = 4$ Square both sides to remove the square root. $x + 1 = 16$ Subtract $1$ from both sides. $x = 15$ Check the answer for extraneous solutions. Does the answer make the original statement true? $\sqrt {15+1} = 4$ $\sqrt{16} = 4$ $4 = 4$ Since the statement is true, we can conclude that $x = 15$.