Evaluate fourth root of 80

Problem

√(4,80)

Solution

1. Identify the prime factorization of the radicand 80

80=2⋅2⋅2⋅2⋅5

80=2⋅5

2. Apply the property of radicals that states √(n,a⋅b)=√(n,a)⋅√(n,b)

√(4,2⋅5)=√(4,2)⋅√(4,5)

3. Simplify the radical expression by evaluating the fourth root of the perfect fourth power.

√(4,2)=2

4. Combine the simplified parts to reach the final radical form.

2⋅√(4,5)

Final Answer

√(4,80)=2√(4,5)

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