Evaluate cube root of 72

Problem

√(3,72)

Solution

1. Factor the number inside the radical into its prime factors.

72=8×9

72=2×3

2. Apply the property of radicals √(n,a×b)=√(n,a)×√(n,b) to separate the perfect cube.

√(3,2×3)=√(3,2)×√(3,3)

3. Simplify the cube root of the perfect cube.

√(3,2)=2

4. Combine the simplified coefficient with the remaining radical.

2×√(3,3)=2√(3,9)

Final Answer

√(3,72)=2√(3,9)

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