Questions: 7 sqrt(12) * 2 sqrt(2) simplifies to sqrt(6)

Solution Steps

First, simplify the expression \(7 \sqrt{12} \cdot 2 \sqrt{2}\).

Simplify \(\sqrt{12}\) and \(\sqrt{2}\):

\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \]

\[ \sqrt{2} = \sqrt{2} \]

Substitute the simplified square roots back into the expression:

\[ 7 \cdot 2\sqrt{3} \cdot 2 \cdot \sqrt{2} = 7 \cdot 2 \cdot 2 \cdot \sqrt{3} \cdot \sqrt{2} \]

Combine the constants and the square roots:

\[ 7 \cdot 2 \cdot 2 = 28 \]

\[ \sqrt{3} \cdot \sqrt{2} = \sqrt{6} \]

Thus, the expression becomes:

\[ 28 \sqrt{6} \]

Final Answer