Express in simplest radical form. $$ -9 \sqrt{90}-\sqrt{160} $$

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UpStudy AI · Accepted Answer

We start by simplifying each radical:

1. Simplify $$ \sqrt{90} $$:
   $$
   \sqrt{90} = \sqrt{9\cdot10} = \sqrt{9}\sqrt{10} = 3\sqrt{10}
   $$
   So,
   $$
   -9 \sqrt{90} = -9(3\sqrt{10}) = -27\sqrt{10}
   $$

2. Simplify $$ \sqrt{160} $$:
   $$
   \sqrt{160} = \sqrt{16\cdot10} = \sqrt{16}\sqrt{10} = 4\sqrt{10}
   $$
   So,
   $$
   -\sqrt{160} = -4\sqrt{10}
   $$

3. Combine the simplified terms:
   $$
   -27\sqrt{10} - 4\sqrt{10} = (-27 - 4)\sqrt{10} = -31\sqrt{10}
   $$

Thus, the expression in simplest radical form is:
$$
-31\sqrt{10}
$$
$$ -31\sqrt{10} $$

Express in simplest radical form.

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