Question

express in simplest radical form.
$-4\sqrt{45} - 10\sqrt{80}$
answer
attempt 1 out of 2
submit answer

Explanation:

Step1: Simplify each radical

First, simplify \(\sqrt{45}\). We know that \(45 = 9\times5\), and \(\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}=3\sqrt{5}\). So, \(- 4\sqrt{45}=-4\times3\sqrt{5}=-12\sqrt{5}\).

Next, simplify \(\sqrt{80}\). Since \(80 = 16\times5\), then \(\sqrt{16\times5}=\sqrt{16}\times\sqrt{5}=4\sqrt{5}\). So, \(-10\sqrt{80}=-10\times4\sqrt{5}=-40\sqrt{5}\).

Step2: Combine like terms

Now we have \(-12\sqrt{5}-40\sqrt{5}\). Since the radicals are the same (\(\sqrt{5}\)), we can combine the coefficients: \((- 12-40)\sqrt{5}=-52\sqrt{5}\).

Answer:

\(-52\sqrt{5}\)