Evaluate - fourth root of 625

Problem

√(4,625)

Solution

1. Identify the number whose fourth power equals the radicand, 625

2. Factor the number 625 into its prime factors to see the underlying structure.

625=5×125

625=5×5×25

625=5×5×5×5

3. Rewrite the expression using exponents to simplify the radical.

625=5

4. Apply the property of radicals √(n,an)=a for positive real numbers.

√(4,5)=5

Final Answer

√(4,625)=5

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