Calculate the square root of 42

Problem

√(,42)

Solution

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

2. Factor the number into its prime factors to see if it contains any perfect squares.

42=2⋅3⋅7

3. Determine if the expression can be simplified. Since there are no repeating prime factors, 42 has no square factors other than 1

4. Conclude that the square root cannot be simplified into a simpler radical form.

5. Estimate the decimal value if needed. Since 6=36 and 7=49 the value is between 6 and 7

√(,42)≈6.48074

Final Answer

√(,42)=√(,42)

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