Simplify cube root of 216

Problem

√(3,216)

Solution

1. Identify the number inside the radical, which is 216

2. Find the prime factorization of the number to see if it is a perfect cube.

216=2⋅108

108=2⋅54

54=2⋅27

27=3⋅9

9=3⋅3

3. Group the factors into sets of three to express the number as a power of 3

216=2⋅3

216=(2⋅3)3

216=6

4. Apply the property of radicals where √(n,an)=a for any real number a when n is odd.

√(3,6)=6

Final Answer

√(3,216)=6

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