#### Answer

$x=\frac{5}{4}$

#### Work Step by Step

$\displaystyle \sqrt{8x-1}=3$
$(\sqrt{8x-1})^{2}=3^{2}$
$8x-1=9$
$8x=9+1=10$
$x=\frac{10}{8}$
$x=\frac{5}{4}$
We need to confirm that the solution $x=\frac{5}{4}$ works in the original equation:
$\sqrt{8(\frac{5}{4})-1}=\sqrt{10-1}=\sqrt{9}=3$
Which is true.