Evaluate fifth root of 53

Problem

√(5,53)

Solution

1. Identify the expression as the fifth root of the number 53 which can be written in exponent form as 53(1/5)

2. Determine if 53 is a perfect fifth power. Since 2=32 and 3=243 the value must be a decimal between 2 and 3

3. Approximate the value using numerical methods or a calculator, as 53 is a prime number and cannot be simplified further in radical form.

4. Calculate the decimal expansion to several places.

Final Answer

√(5,53)≈2.21236

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