Calculate the square root of 30

Problem

√(,30)

Solution

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

2. Determine the prime factorization of the radicand to see if it contains any perfect square factors.

3. Factor the number: 30=2⋅3⋅5

4. Observe that there are no repeating prime factors, meaning 30 has no perfect square factors other than 1

5. Conclude that the expression cannot be simplified further in radical form.

6. Approximate the value if a decimal is required by noting that 5=25 and 6=36 so the value lies between 5 and 6

Final Answer

√(,30)≈5.477

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