To perform the operation \(\sqrt{6} \cdot \sqrt{8}\), we first use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\).
So, we have:
\[ \sqrt{6} \cdot \sqrt{8} = \sqrt{6 \cdot 8} \]
Calculating the product inside the square root:
\[ 6 \cdot 8 = 48 \]
Thus, we have:
\[ \sqrt{6} \cdot \sqrt{8} = \sqrt{48} \]
Next, we simplify \(\sqrt{48}\). We can factor 48 into its prime factors:
\[ 48 = 16 \cdot 3 = 4^2 \cdot 3 \]
Now we can take the square root:
\[ \sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3} \]
Therefore, the exact simplified answer is:
\[ \sqrt{6} \cdot \sqrt{8} = 4\sqrt{3} \]
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