Simplify cube root of 24

Problem

√(3,24)

Solution

1. Identify the prime factorization of the number inside the radical.

24=2⋅2⋅2⋅3

2. Group the factors into sets of three, since we are finding a cube root.

24=2⋅3

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

√(3,24)=√(3,2)⋅√(3,3)

4. Simplify the cube root of the perfect cube.

√(3,2)=2

5. Combine the terms to find the final simplified form.

2⋅√(3,3)

Final Answer

√(3,24)=2√(3,3)

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