Simplify cube root of 24 cube root of 18

Problem

√(3,24)⋅√(3,18)

Solution

1. Apply the product property of radicals to combine the two cube roots into a single radical.

√(3,a)⋅√(3,b)=√(3,a⋅b)

√(3,24⋅18)

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

24=2^3⋅3

18=2⋅3^2

3. Multiply the factors inside the radical by adding the exponents of like bases.

√(3,(2^3⋅3)⋅(2⋅3^2))

√(3,2^4⋅3^3)

4. Rewrite the powers to isolate perfect cubes (powers of 3).

√(3,2^3⋅2^1⋅3^3)

5. Simplify the radical by taking the cube root of the perfect cubes.

2⋅3⋅√(3,2)

6√(3,2)

Final Answer

√(3,24)⋅√(3,18)=6√(3,2)

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