Question

Adding /subtracting radicals
-4√160-2√90

Answer 1

To simplify the expression \(-4\sqrt{160} - 2\sqrt{90}\), we first break down each radical.

### Step 1: Simplify \(\sqrt{160}\)
\[
160 = 16 \times 10 = 4^2 \times 10
\]
So,
\[
\sqrt{160} = \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10} = 4\sqrt{10}
\]
Thus,
\[
-4\sqrt{160} = -4(4\sqrt{10}) = -16\sqrt{10}
\]

### Step 2: Simplify \(\sqrt{90}\)
\[
90 = 9 \times 10 = 3^2 \times 10
\]
So,
\[
\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}
\]
Thus,
\[
-2\sqrt{90} = -2(3\sqrt{10}) = -6\sqrt{10}
\]

### Step 3: Combine the simplified terms
Now we combine \(-16\sqrt{10}\) and \(-6\sqrt{10}\):
\[
-16\sqrt{10} - 6\sqrt{10} = (-16 - 6)\sqrt{10} = -22\sqrt{10}
\]

### Final Answer:
The simplified result is
\[
\boxed{-22\sqrt{10}}
\]