Evaluate cube root of 24

Problem

√(3,24)

Solution

1. Identify the radicand and look for perfect cube factors.

2. Factor the number 24 into its prime factors or a product involving a perfect cube.

24=8⋅3

3. Recognize that 8 is a perfect cube because 2=8

4. Apply the product property of radicals, which states √(3,a⋅b)=√(3,a)⋅√(3,b)

√(3,8⋅3)=√(3,8)⋅√(3,3)

5. Simplify the cube root of the perfect cube.

√(3,8)=2

6. Combine the results to find the simplified radical form.

2⋅√(3,3)

Final Answer

√(3,24)=2√(3,3)

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