Evaluate

Problem

3√(,14)⋅(2√(,21))

Solution

1. Group the coefficients and the radicals using the associative and commutative properties of multiplication.

3⋅2⋅√(,14)⋅√(,21)

2. Multiply the coefficients outside the radical.

6⋅√(,14)⋅√(,21)

3. Combine the radicals using the product property √(,a)⋅√(,b)=√(,a⋅b)

6√(,14⋅21)

4. Factor the numbers inside the radical to identify perfect squares.

6√(,(2⋅7)⋅(3⋅7))

5. Simplify the radicand by grouping the pair of 7s.

6√(,2⋅3⋅7)

6. Extract the square root of the perfect square 7

6⋅7√(,2⋅3)

7. Multiply the remaining values to find the final simplified form.

42√(,6)

Final Answer

3√(,14)⋅(2√(,21))=42√(,6)

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