Calculate the square root of 37

Problem

√(,37)

Solution

1. Identify the number as a non-perfect square. Since 6=36 and 7=49 the value of √(,37) is an irrational number slightly greater than 6

2. Estimate using the linear approximation formula √(,x+h)≈√(,x)+h/(2√(,x)) Let x=36 and h=1

3. Calculate the approximation: √(,37)≈6+1/(2*(6))=6+1/12≈6.0833

4. Determine the exact form. Since 37 is a prime number, the square root cannot be simplified into a product of an integer and a smaller radical.

Final Answer

√(,37)≈6.08276253

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