Evaluate cube root of 54

Problem

√(3,54)

Solution

1. Identify the number under the radical and look for its prime factorization.

54=2⋅27

2. Recognize that 27 is a perfect cube.

27=3

3. Rewrite the expression using the prime factors.

√(3,2⋅3)

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

√(3,3)⋅√(3,2)

5. Simplify the cube root of the perfect cube.

3⋅√(3,2)

Final Answer

√(3,54)=3√(3,2)

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