Calculate the square root of 65

Problem

√(,65)

Solution

1. Identify the number under the radical, which is 65

2. Determine if 65 is a perfect square. Since 8=64 and 9=81 the square root is not an integer.

3. Factor the number to see if it can be simplified. The prime factorization of 65 is 5×13

4. Conclude that since there are no repeated prime factors, the radical cannot be simplified further into the form a√(,b)

5. Estimate the decimal value. Since 65 is slightly larger than 64 the value is slightly larger than 8

Final Answer

√(,65)≈8.0622577

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