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Solving an equation involves finding the value of an unknown variable that satisfies the equation. The goal is to manipulate the equation until you isolate the variable on one side, showing what it equals on the other side. This is achieved by performing operations that "undo" what is currently being done to the variable.
For example, if you have an equation like \(C = 3 + x\), you would subtract 3 from both sides to solve for \(x\), resulting in \(x = C - 3\). This process of simplification continues until the variable is adequately isolated.
Throughout this solving process, maintaining balance is crucial. This means whatever operation you do to one side of the equation, you must also do to the other side. This ensures the equality is preserved, which is fundamental in algebra.

Isolating the variable is about getting the variable by itself on one side of the equation. This often requires undoing arithmetic operations, such as addition, subtraction, multiplication, or division, impacting the variable.
In the given problem, \(L = \frac{2U}{I^2}\), the goal is to get \(I\) by itself. Initially, you multiply both sides by \(I^2\) to eliminate the fraction. This results in \(LI^2 = 2U\).
Once simplified, \(I^2\) becomes the isolated term, with \(I\) not quite alone yet. Sometimes, more than one step, like dividing another term, is necessary to completely isolate the variable. The solution proceeds by dividing both sides by \(L\), so \(I\) is isolated to the extent that its square can be addressed.

Taking the square root of both sides is a common step when solving equations involving squared variables. It helps to find the actual value of the variable by reversing the squaring operation.
In our equation, once isolated, \(I^2 = \frac{2U}{L}\), the next step is applying the square root to solve for \(I\). Mathematically, if \(I^2 = a\), then \(I = \pm \sqrt{a}\). However, since \(I\) represents a magnitude like current, we typically consider only the positive root, \(I = \sqrt{\frac{2U}{L}}\).
Remember, taking the square root is crucial in converting a squared term to a simple linear term, allowing you to express the variable explicitly. This step is key in moving from a more complex form to a practical and usable solution.