Evaluate fourth root of 48

Problem

√(4,48)

Solution

1. Identify the radicand and the index of the root. The radicand is 48 and the index is 4

2. Find the prime factorization of the number 48

48=2⋅24

48=2⋅2⋅12

48=2⋅2⋅2⋅6

48=2⋅2⋅2⋅2⋅3

48=2⋅3

3. Apply the product property of radicals, which states √(n,a⋅b)=√(n,a)⋅√(n,b)

√(4,2⋅3)=√(4,2)⋅√(4,3)

4. Simplify the radical by evaluating the fourth root of the perfect fourth power.

√(4,2)=2

5. Combine the simplified terms into the final radical expression.

2⋅√(4,3)

Final Answer

√(4,48)=2√(4,3)

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