Simplify cube root of 81

Problem

√(3,81)

Solution

1. Factor the radicand into its prime factors.

81=3⋅3⋅3⋅3

2. Group the factors into sets of three, as the index of the radical is 3.

81=3⋅3

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

√(3,3⋅3)=√(3,3)⋅√(3,3)

4. Simplify the cube root of the perfect cube.

√(3,3)=3

Final Answer

√(3,81)=3√(3,3)

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