Calculate the square root of 103

Problem

√(,103)

Solution

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

2. Estimate the value by finding the nearest perfect squares, which are 100 (10 and 121 (11.

3. Determine that the value lies between 10 and 11 specifically very close to 10 since 103 is close to 100

4. Calculate the decimal approximation using a calculator or numerical methods like Newton's method.

5. Round the result to a standard number of decimal places, such as four.

Final Answer

√(,103)≈10.1489

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