\( \begin{array}{lllll}\text { (d) } \sqrt{3 x-2}-x=0 & \text { (e) } x+\sqrt{-4 x-3}=0 & \text { (f) } \sqrt{x+2}+4=x \\ \text { (g) } \sqrt{4-2 x}-\sqrt{x+1}=0 & \text { (h) } \sqrt{5-x}+1+x=0 & \text { (i) } \sqrt{x+5} \cdot \sqrt{x-2}=3 \sqrt{2}\end{array} \)

Let’s dive into some fun insights about solving equations like the ones you’ve presented! When dealing with equations that involve square roots, one key historical figure comes to mind: the Indian mathematician Brahmagupta, who was instrumental in developing rules for manipulating equations, including finding solutions involving square roots. His work laid the groundwork for algebra as we know it today! So, next time you're solving a radical equation, channel your inner Brahmagupta and remember how far mathematics has come! Now, onto practical tips! Always remember to isolate the square root on one side before squaring both sides of an equation. It might sound simple, but common mistakes often arise when squaring; they can introduce extraneous solutions! For example, in your equation \( \sqrt{3x-2}-x=0 \), isolating the square root first ensures you’re on the right track. Fact-check your answers carefully to avoid the pesky traps that come from squaring both sides!