Simplify the expression. Leave your answer In simplest radical form. (sqrt (6))(sqrt (30)) square

To simplify the expression \((\sqrt{6})(\sqrt{30})\), we can use the property of square roots that states:<br /><br />\[<br />\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}<br />\]<br /><br />Applying this property to our expression, we get:<br /><br />\[<br />(\sqrt{6})(\sqrt{30}) = \sqrt{6 \cdot 30}<br />\]<br /><br />Next, we multiply the numbers inside the square root:<br /><br />\[<br />6 \cdot 30 = 180<br />\]<br /><br />So, we have:<br /><br />\[<br />\sqrt{6 \cdot 30} = \sqrt{180}<br />\]<br /><br />Now, we need to simplify \(\sqrt{180}\). To do this, we factor \(180\) into its prime factors:<br /><br />\[<br />180 = 2^2 \cdot 3^2 \cdot 5<br />\]<br /><br />Using the property of square roots, we can separate the factors:<br /><br />\[<br />\sqrt{180} = \sqrt{2^2 \cdot 3^2 \cdot 5} = \sqrt{2^2} \cdot \sqrt{3^2} \cdot \sqrt{5}<br />\]<br /><br />Since \(\sqrt{2^2} = 2\) and \(\sqrt{3^2} = 3\), we get:<br /><br />\[<br />\sqrt{180} = 2 \cdot 3 \cdot \sqrt{5} = 6\sqrt{5}<br />\]<br /><br />Therefore, the simplified form of the expression \((\sqrt{6})(\sqrt{30})\) is:<br /><br />\[<br />6\sqrt{5}<br />\]