Evaluate 3 square root of 6

Problem

3√(,6)

Solution

1. Identify the expression as a product of a constant and a square root.

2. Determine if the radicand, 6, has any perfect square factors other than 1.

3. Observe that the prime factorization of 6 is 2×3 which contains no pairs of prime factors.

4. Conclude that the expression is already in its simplest radical form.

5. Approximate the value if a decimal is required by calculating √(,6)≈2.449

6. Multiply the constant by the approximation: 3×2.449≈7.348

Final Answer

3√(,6)≈7.348469

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