Explain why it is sometimes necessary to express square roots in their simplest radical form. Then, explain the process of rewriting a square root in its simplest radical form.

Question

in 3 to 5 sentences

Answer 1

Expressing square roots in their simplest radical form is important for clarity and ease of understanding, particularly in mathematics, as it allows for easier manipulation and comparison of expressions. Simplifying square roots can help identify values that can be further simplified in equations or functions. To rewrite a square root in its simplest form, you factor the number inside the square root into its prime factors, extract any perfect squares, and write the expression as a product of the square root of the perfect square and the square root of the remaining factors. For example, \(\sqrt{24}\) can be simplified as \(\sqrt{4 \cdot 6}\), which results in \(2\sqrt{6}\).