Question

Express in simplest radical form.
minus, 4, square root of, 45, end square root, minus, 10, square root of, 80, end square root
−4
45
​
−10
80
​

Answer
Attempt 1 out of 5

Answer 1

To simplify the expression \(-4\sqrt{45} - 10\sqrt{80}\), we'll start by simplifying each square root separately.

1. **Simplifying \(\sqrt{45}\):**
\[
\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}
\]

2. **Simplifying \(\sqrt{80}\):**
\[
\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}
\]

Now, we can substitute these simplified square roots back into the expression:

\[
-4\sqrt{45} - 10\sqrt{80} = -4(3\sqrt{5}) - 10(4\sqrt{5})
\]

Calculating these terms yields:

\[
-4(3\sqrt{5}) = -12\sqrt{5}
\]
\[
-10(4\sqrt{5}) = -40\sqrt{5}
\]

Now, combine the two results:

\[
-12\sqrt{5} - 40\sqrt{5} = (-12 - 40)\sqrt{5} = -52\sqrt{5}
\]

Thus, the expression in simplest radical form is:

\[
\boxed{-52\sqrt{5}}
\]