Simplify square root of 30

Problem

√(,30)

Solution

1. Identify the number under the radical, which is 30

2. Find the prime factorization of the radicand to see if there are any perfect square factors.

30=2⋅3⋅5

3. Check for pairs of identical factors. Since all prime factors (2 3 and 5 appear only once, there are no perfect square factors other than 1

4. Conclude that the radical cannot be simplified further into a form a√(,b) where b is a smaller integer.

Final Answer

√(,30)=√(,30)

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