Evaluate square root of 42

Problem

√(,42)

Solution

1. Identify the number under the radical, which is 42

2. Determine the prime factorization of the radicand to see if it can be simplified.

3. Factor 42 into its prime components: 42=2×3×7

4. Observe that there are no perfect square factors (pairs of prime factors) in the factorization.

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

6. Approximate the value if a decimal is required: since 6=36 and 7=49 the value is between 6 and 7

Final Answer

√(,42)=√(,42)

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