Final answer:
A radical is not in simplest form if it contains a perfect square within the radical. By factoring out the perfect squares, the expression is simplified. It's crucial to be adept at simplifying radicals and using the Pythagorean Theorem in relevant contexts.
Step-by-step explanation:
The reason a radical expression may not be in its simplest form is because it contains a perfect square within the radical. To simplify such an expression, we identify the perfect square factors under the radical and rewrite them outside the radical sign. Taking the square root of a perfect square eliminates the radical, resulting in a simpler expression.
For example, in an equation or a problem involving square roots, such as finding the side length of a right triangle given the other sides, the Pythagorean Theorem is used, followed by taking the square root to solve for the missing side length. Similarly, in an expression like -13 ± √(13)² - 4 × 3 × (−10), we need to simplify the radical to find the simplest form for the solution.
It's essential to understand how to simplify radicals and perform such operations, either manually or with a calculator, especially when dealing with equilibrium problems or when invert mathematical functions.