Evaluate 3 cube root of 16

Problem

3√(3,16)

Solution

1. Identify the radicand and look for perfect cube factors. The number 16 can be factored into 8×2

2. Apply the property of radicals that states √(n,a*b)=√(n,a)⋅√(n,b)

3√(3,16)=3√(3,8⋅2)

3. Separate the radical into the product of two radicals.

3√(3,8⋅2)=3√(3,8)⋅√(3,2)

4. Evaluate the cube root of the perfect cube. Since 2=8 it follows that √(3,8)=2

3⋅2⋅√(3,2)

5. Multiply the coefficients outside the radical.

6√(3,2)

Final Answer

3√(3,16)=6√(3,2)

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