Simplify each radical expressing 8. 5sqrt (150)

To simplify the radical expression \(5\sqrt{150}\), we need to factor the number under the square root and then simplify the radical.<br /><br />First, let's factor 150:<br />\[ 150 = 2 \times 3 \times 5^2 \]<br /><br />Now, we can rewrite the radical expression:<br />\[ 5\sqrt{150} = 5\sqrt{2 \times 3 \times 5^2} \]<br /><br />Next, we can use the property of square roots that states \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\):<br />\[ 5\sqrt{2 \times 3 \times 5^2} = 5 \times \sqrt{2 \times 3} \times \sqrt{5^2} \]<br /><br />We know that \(\sqrt{5^2} = 5\), so we can simplify further:<br />\[ 5 \times \sqrt{2 \times 3} \times 5 = 5 \times 5 \times \sqrt{6} = 25\sqrt{6} \]<br /><br />Therefore, the simplified form of \(5\sqrt{150}\) is:<br />\[ 5\sqrt{150} = 25\sqrt{6} \]