Evaluate cube root of 80

Problem

√(3,80)

Solution

1. Identify the prime factorization of the radicand 80

80=2×2×2×2×5

80=2×5

2. Rewrite the expression by grouping the factors into a perfect cube.

√(3,2×2×5)

3. Apply the property of radicals √(3,a×b)=√(3,a)×√(3,b) to separate the perfect cube.

√(3,2)×√(3,2×5)

4. Simplify the cube root of the perfect cube and multiply the remaining factors under the radical.

2×√(3,10)

Final Answer

√(3,80)=2√(3,10)

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