Question

sqrt8-sqrt32

Answer 1

To simplify the expression \(\sqrt{8} - \sqrt{32}\), we start by simplifying each square root.

1. **Simplifying \(\sqrt{8}\)**:
\[
\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\]

2. **Simplifying \(\sqrt{32}\)**:
\[
\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}
\]

Now, substituting back into the expression:
\[
\sqrt{8} - \sqrt{32} = 2\sqrt{2} - 4\sqrt{2}
\]

Combine the terms:
\[
2\sqrt{2} - 4\sqrt{2} = (2 - 4)\sqrt{2} = -2\sqrt{2}
\]

Thus, the final result is:
\[
\sqrt{8} - \sqrt{32} = -2\sqrt{2}
\]