Evaluate cube root of 108

Problem

√(3,108)

Solution

1. Find the prime factorization of the number 108 to identify perfect cube factors.

108=2⋅54

108=2⋅2⋅27

108=2⋅3

2. Rewrite the expression using the prime factorization inside the radical.

√(3,108)=√(3,3⋅2)

3. Apply the product property of radicals to separate the perfect cube from the remaining factors.

√(3,3⋅4)=√(3,3)⋅√(3,4)

4. Simplify the radical by taking the cube root of the perfect cube.

√(3,3)⋅√(3,4)=3√(3,4)

Final Answer

√(3,108)=3√(3,4)

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