Question

1. rewrite the following expression in simplest radical form.\\(\sqrt{30} =\\) \\(\boxed{}\\)

Explanation:

Step1: Factorize 30

To simplify \(\sqrt{30}\), we first factorize 30. The prime factorization of 30 is \(30 = 2\times3\times5\).

Step2: Check for perfect square factors

A perfect square factor is a factor that is a square of an integer. In the prime factorization of 30 (\(2\times3\times5\)), there are no perfect square factors (since 2, 3, and 5 are all prime numbers and their exponents in the factorization are 1, which is less than 2).

Step3: Conclusion

Since there are no perfect square factors other than 1, \(\sqrt{30}\) is already in its simplest radical form.

Answer:

\(\sqrt{30}\)