Simplify fourth root of 162

Problem

√(4,162)

Solution

1. Find the prime factorization of the radicand 162

162=2⋅81

162=2⋅3

2. Apply the property of radicals √(n,a⋅b)=√(n,a)⋅√(n,b) to separate the factors.

√(4,162)=√(4,3⋅2)

√(4,162)=√(4,3)⋅√(4,2)

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

√(4,3)=3

4. Combine the terms to write the expression in simplest radical form.

3⋅√(4,2)

Final Answer

√(4,162)=3√(4,2)

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