When rewriting inequalities it's important to make the the same operation on both sides to ensure that the inequality still holds. If one side is raised to a power, the same operation must be performed on the other side. In the inequality sqrt(x) ≤ 8, both sides can be raised to the power of 2. (sqrt(x))^2 ≤ 8^2 However, this operation should only be used when the bases on both sides are positive. Otherwise, we need to divide the inequality into cases and check absolute values.