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When solving equations with square roots, one of the first steps is to isolate the variable. This means that you want to get the square root term that contains the variable on one side of the equation by itself. To achieve this, you may have to move other terms to the opposite side of the equation.

For example, in the equation \( \sqrt{3t+11} - 5\sqrt{t} = 0 \) from the exercise, thee terms involving square roots are on the same side. To isolate the square root containing the variable 't', you can add \( 5\sqrt{t} \) to both sides, resulting in \(( \sqrt{3t+11} = 5\sqrt{t} ))\). Now, you have successfully isolated the square root on one side, which makes it easier to deal with the equation moving forward.

After isolating one of the square roots, the next step in solving square root equations is to eliminate the square root itself. This is done by squaring both sides of the equation. It's important to remember that when you square a square root, you're left with just the value under the root sign.

In our example, when you square \( \sqrt{3t+11} \) and \( 5\sqrt{t} \), you end up with \( (\sqrt{3t+11})^2 = (5\sqrt{t})^2 \) which simplifies to \( 3t + 11 = 25t \). By doing this, we have efficiently removed the square roots from the equation, transforming it into a simpler form that can be solved using algebraic methods.

Solving equations that include square roots can seem daunting, but it's a matter of recognizing the patterns and applying the right steps. After isolating the variable and squaring both sides, it's typical to end up with an equation without any square roots.

Continuing with our example, after simplifying, you get \( 11 = 22t \) from the squared equation \( 3t + 11 = 25t \). The final step is straightforward: divide both sides by 22 to solve for 't', yielding \( t = \frac{11}{22} = 0.5 \). So, in essence, while equations with square roots initially look complicated, they can be tackled efficiently by understanding how to manipulate and eliminate the square root to arrive at the solution.