Simplify cube root of 54

Problem

√(3,54)

Solution

1. Find the prime factorization of the number inside the radical to identify perfect cubes.

54=2⋅27

54=2⋅3

2. Apply the product property of radicals to separate the perfect cube from the remaining factor.

√(3,2⋅3)=√(3,3)⋅√(3,2)

3. Simplify the radical by evaluating the cube root of the perfect cube.

√(3,3)=3

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

3⋅√(3,2)

Final Answer

√(3,54)=3√(3,2)

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