Evaluate cube root of 24 cube root of 18

Problem

√(3,24)⋅√(3,18)

Solution

1. Combine the radicals using the product property of radicals, √(n,a)⋅√(n,b)=√(n,a⋅b)

√(3,24⋅18)

2. Factor the numbers inside the radical into their prime factors to identify perfect cubes.

24=2⋅3

18=2⋅3

3. Multiply the prime factors together.

24⋅18=(2⋅3)⋅(2⋅3)

24⋅18=2⋅3

4. Rewrite the expression to group perfect cubes.

√(3,2⋅2⋅3)

5. Simplify by taking the cube root of the perfect cubes 2 and 3

2⋅3⋅√(3,2)

6. Multiply the coefficients outside the radical.

6√(3,2)

Final Answer

√(3,24)⋅√(3,18)=6√(3,2)

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