Evaluate cube root of 16

Problem

√(3,16)

Solution

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

2. Factor the number 16 into its prime components.

16=2×2×2×2

16=2

3. Rewrite the expression using the property of exponents where √(n,am)=a(m/n)

√(3,2)=2(4/3)

4. Simplify the radical by pulling out the largest perfect cube.

√(3,2×2)

√(3,2)×√(3,2)

2×√(3,2)

Final Answer

√(3,16)=2√(3,2)

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