Question

Express in simplest radical form.
6, square root of, 160, end square root, minus, square root of, 40, end square root
6
160
​
−
40
​

Answer
Attempt 1 out of 5

Submit Answer
square root of, end square root
x
​

Answer 1

To simplify the expression \( 6\sqrt{160} - \sqrt{40} \), we will simplify each square root first.

1. **Simplifying \( \sqrt{160} \)**:
\[
\sqrt{160} = \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10} = 4\sqrt{10}
\]

2. **Simplifying \( \sqrt{40} \)**:
\[
\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}
\]

Now we can substitute these simplified forms back into the original expression:

\[
6\sqrt{160} - \sqrt{40} = 6(4\sqrt{10}) - 2\sqrt{10}
\]

3. **Calculating \( 6(4\sqrt{10}) \)**:
\[
6(4\sqrt{10}) = 24\sqrt{10}
\]

4. **Substituting back**:
\[
24\sqrt{10} - 2\sqrt{10}
\]

5. **Combining like terms**:
\[
(24 - 2)\sqrt{10} = 22\sqrt{10}
\]

Thus, the expression simplified in its simplest radical form is:

\[
\boxed{22\sqrt{10}}
\]