Evaluate 4 cube root of 24

Problem

4√(3,24)

Solution

1. Identify the radicand, which is 24 and look for its prime factorization.

24=2⋅2⋅2⋅3

24=2⋅3

2. Rewrite the cube root by substituting the prime factorization into the expression.

4√(3,2⋅3)

3. Apply the property of radicals √(n,a⋅b)=√(n,a)⋅√(n,b) to separate the perfect cube.

4⋅√(3,2)⋅√(3,3)

4. Simplify the cube root of the perfect cube, noting that √(3,2)=2

4⋅2⋅√(3,3)

5. Multiply the coefficients outside the radical.

8√(3,3)

Final Answer

4√(3,24)=8√(3,3)

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