Evaluate cube root of 192

Problem

√(3,192)

Solution

1. Identify the number under the radical and look for perfect cube factors.

2. Factor the number 192 into its prime factors or find the largest perfect cube that divides it.

192=64×3

3. Recognize that 64 is a perfect cube because 4=64

4. Apply the product property of radicals to separate the cube root of the product into the product of the cube roots.

√(3,64×3)=√(3,64)×√(3,3)

5. Simplify the cube root of the perfect cube.

√(3,64)=4

6. Combine the results to write the expression in simplest radical form.

4×√(3,3)=4√(3,3)

Final Answer

√(3,192)=4√(3,3)

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