Evaluate square root of 37

Problem

√(,37)

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, which are 36 and 49

3. Determine that since 36<37<49 the value of √(,37) must be between √(,36)=6 and √(,49)=7

4. Approximate the decimal value using a calculator or numerical methods like Newton's method.

5. Conclude that the exact form is √(,37) and the approximate decimal form is 6.08276...

Final Answer

√(,37)≈6.08276253

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