To simplify the expression \(2\sqrt{18} \cdot 6\sqrt{7}\), we will first simplify \(2\sqrt{18}\) and then combine it with \(6\sqrt{7}\).
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Simplifying \( \sqrt{18} \): \[ \sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2} \] So, \[ 2\sqrt{18} = 2 \cdot 3\sqrt{2} = 6\sqrt{2} \]
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Now, replacing \( 2\sqrt{18} \) in the expression: \[ 2\sqrt{18} \cdot 6\sqrt{7} = 6\sqrt{2} \cdot 6\sqrt{7} \]
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Combining the terms: \[ (6 \cdot 6)(\sqrt{2} \cdot \sqrt{7}) = 36 \sqrt{14} \]
Thus, the product of the expression in simplest radical form is: \[ \boxed{36\sqrt{14}} \]
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