Evaluate square root of 10

Problem

√(,10)

Solution

1. Identify the expression as the square root of a non-perfect square integer.

2. Determine if the radicand has any perfect square factors. Since the prime factorization of 10 is 2×5 there are no perfect square factors to simplify.

3. Approximate the value using a calculator or numerical methods. Since 3=9 and 4=16 the value is slightly greater than 3

4. Calculate the decimal expansion to several places.

Final Answer

√(,10)≈3.16227766

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