Answer
$\dfrac{1}{25}$
Work Step by Step
Subtract $7$ from both sides:
$$5\sqrt{x}+7-7=8-7$$
$$5\sqrt{x}=1$$
Divide both sides by $5$:
$$\frac{5\sqrt{x}}{5}=\frac{1}{5}$$
$$\sqrt{x}=\frac15$$
Square both sides:
$$(\sqrt{x})^2=\left(\frac15\right)^2$$
$$x=\frac{1}{25}$$
Substitute into original problem to check for extraneous solutions:
$$5\sqrt{\left(\frac{1}{25}\right)}+7=8$$
$$5\left(\frac15\right)+7=8$$
$$1+7=8$$
$$8=8$$
