Evaluate cube root of 625

Problem

√(3,625)

Solution

1. Identify the number inside the radical and look for its prime factorization.

2. Factor the number 625 into its prime components.

625=5×125

625=5×5×25

625=5×5×5×5

625=5

3. Rewrite the expression using the prime factorization.

√(3,625)=√(3,5)

4. Simplify the radical by pulling out groups of three, since the index of the root is 3

√(3,5×5)

5√(3,5)

Final Answer

√(3,625)=5√(3,5)

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