Evaluate 8 square root of 2

Problem

8√(,2)

Solution

1. Identify the expression as a product of an integer and an irrational number.

2. Determine if the square root can be simplified further. Since 2 is a prime number and has no perfect square factors other than 1 √(,2) is already in its simplest radical form.

3. Approximate the value if a decimal is required. The value of √(,2) is approximately 1.4142

4. Multiply the integer by the approximation: 8×1.4142=11.3136

Final Answer

8√(,2)≈11.3137

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