Chapter 1 - 1.6 - Other Types of Equations - 1.6 Exercises - Page 128: 39

$x=4$

$\sqrt {x-3}+1=\sqrt x$, $\sqrt {x-3}=\sqrt {x} -1$, Squaring both sides: $x-3=x-2\sqrt x +1$, $4-2\sqrt x=0$, $4=2\sqrt x$ $2=\sqrt x$ Squaring both sides: $x=4$ Check: $\sqrt{4-3}+1=2$ $\sqrt 4=2$ $2=2\checkmark$