Evaluate cube root of 216

Problem

√(3,216)

Solution

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

2. Find the prime factorization of 216 to see if it is a perfect cube.

3. Divide 216 by small prime numbers:

216=2×108

108=2×54

54=2×27

27=3×9

9=3×3

4. Group the prime factors into sets of three:

216=2×3

5. Apply the property of exponents (a×b)n=an×bn

216=(2×3)3

216=6

6. Evaluate the cube root by taking the base of the cubed expression:

√(3,6)=6

Final Answer

√(3,216)=6

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