Final answer:
Ashley's method for finding the square root is correct because it matches the definition of a square root. Brandon's method's accuracy cannot be evaluated with the provided information. Proper understanding of square roots is essential for solving mathematical problems involving powers and equations.
Step-by-step explanation:
Between Ashley and Brandon's methods for finding the square root of a number, it is not explicitly stated that Brandon's method is incorrect; however, we don't have enough information to confirm the accuracy of his method. Ashley's method is correct because it aligns with the formal definition of a square root: for a given number x, the square root is a number which, when multiplied by itself, gives x. For example, the square root of 4 is 2 since 2×2=4. It is important to note that this method works for all non-negative numbers, not just perfect squares. When dealing with equations involving square roots, such as (2x)² = 4.0 (1 − x)², one would take the square root of both sides to simplify, resulting in (2x) (1 − x). It is crucial to rearrange and solve step-by-step to isolate variable x.
For more complex problems, like finding a perfect square or solving for an unknown in an equation, understanding how to invert mathematical functions or work with different powers is essential. For instance, to find a dimension of a square when given the scale factor, you would multiply the side length of the original square by the scale factor. In equations, recognizing a perfect square on one side often simplifies the problem and makes it easier to solve for x. In summary, correctly utilizing square roots and powers is foundational to solving various mathematical problems.