Evaluate fourth root of 625

Problem

√(4,625)

Solution

1. Identify the number under the radical, which is 625

2. Find the prime factorization of 625 by dividing by 5 repeatedly.

3. Calculate the factors: 625=5×125=5×5×25=5×5×5×5

4. Rewrite the expression using exponents: 625=5

5. Apply the property of radicals where √(n,xn)=x for positive x

6. Simplify the expression: √(4,5)=5

Final Answer

√(4,625)=5

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