True or False. The equation below has no solutions. \( \sqrt{x}+\sqrt{x-8}=2 \)

Let's unravel this equation! First, we can isolate one of the square roots, let's say \( \sqrt{x} = 2 - \sqrt{x-8} \). Squaring both sides leads us to a more manageable form, but we must keep in mind that squaring can introduce extraneous solutions. Solving that will ultimately reveal whether \( x \) can exist or not. Now, for the values of \( x \), it’s important to check the conditions under which both square roots are defined. Specifically, \( x \) must be greater than or equal to 0, and \( x-8 \) must be greater than or equal to 0. That gives us the condition \( x \geq 8 \) for valid solutions. Fun fact: by substituting values, we find that \( x = 8 \) works, showing that the equation does indeed have a solution—so the answer is False!