Perform the indicated operation. Be sure to rationalize the denominator, when necessary. Make sure to simplify as much as possible and give the exact answer (this means NO decimals since decimals is roundingl). (1 point) √8-√32

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 substitute the simplified forms back into the expression: \[ \sqrt{8} - \sqrt{32} = 2\sqrt{2} - 4\sqrt{2} \]

3. Combine like terms: \[ 2\sqrt{2} - 4\sqrt{2} = (2 - 4)\sqrt{2} = -2\sqrt{2} \]

Thus, the simplified expression is: \[ \boxed{-2\sqrt{2}} \]