Evaluate cube root of 3* cube root of 9

Problem

√(3,3)⋅√(3,9)

Solution

1. Identify the property of radicals that allows the multiplication of roots with the same index.

√(n,a)⋅√(n,b)=√(n,a⋅b)

2. Combine the two cube roots into a single radical by multiplying the radicands.

√(3,3⋅9)

3. Multiply the numbers inside the radical.

√(3,27)

4. Evaluate the cube root of 27 by finding the number that, when cubed, equals 27.

3=27

√(3,27)=3

Final Answer

√(3,3)⋅√(3,9)=3

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