Evaluate square root of 13

Problem

√(,13)

Solution

1. Identify the number as a prime number. Since 13 is prime, its square root cannot be simplified into a product of an integer and a smaller radical.

2. Determine the nature of the value. The square root of 13 is an irrational number, meaning its decimal representation is non-repeating and non-terminating.

3. Estimate the value by finding the nearest perfect squares. Since 3=9 and 4=16 the value of √(,13) must lie between 3 and 4.

4. Calculate the decimal approximation. Using a calculator or numerical methods, the value is approximately 3.60555.

Final Answer

√(,13)≈3.60555

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