Evaluate square root of 31

Problem

√(,31)

Solution

1. Identify the number as a non-perfect square, meaning its square root is an irrational number.

2. Estimate the value by finding the nearest perfect squares. Since 25<31<36 the value must be between √(,25)=5 and √(,36)=6

3. Refine the estimate using the linear approximation formula or a calculator. The value is approximately 5.56776

4. State the result in its simplest radical form, which is √(,31) as it has no square factors, or as a decimal approximation.

Final Answer

√(,31)≈5.56776436283

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