Question

express in simplest radical form.
$9\sqrt{150} + \sqrt{24}$

Explanation:

Step1: Simplify each radical

For \(9\sqrt{150}\), factor 150: \(150 = 25\times6\), so \(\sqrt{150}=\sqrt{25\times6}=\sqrt{25}\times\sqrt{6}=5\sqrt{6}\). Then \(9\sqrt{150}=9\times5\sqrt{6}=45\sqrt{6}\).
For \(\sqrt{24}\), factor 24: \(24 = 4\times6\), so \(\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}\).

Step2: Combine like radicals

Now we have \(45\sqrt{6}+2\sqrt{6}\). Since the radicals are the same, we add the coefficients: \((45 + 2)\sqrt{6}=47\sqrt{6}\).

Answer:

\(47\sqrt{6}\)