Add 2√8+3√8–√ .(1 point)

1 answer

To simplify the expression \(2\sqrt{8} + 3\sqrt{8} - \sqrt{8}\), first, we can combine the like terms.

  1. Combine \(2\sqrt{8}\) and \(3\sqrt{8}\): \[ 2\sqrt{8} + 3\sqrt{8} = (2 + 3)\sqrt{8} = 5\sqrt{8} \]

  2. Now, subtract \(\sqrt{8}\): \[ 5\sqrt{8} - \sqrt{8} = (5 - 1)\sqrt{8} = 4\sqrt{8} \]

  3. We can simplify \(\sqrt{8}\): \[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \]

  4. Now substitute \(\sqrt{8}\) back in: \[ 4\sqrt{8} = 4(2\sqrt{2}) = 8\sqrt{2} \]

So the simplified result of \(2\sqrt{8} + 3\sqrt{8} - \sqrt{8}\) is: \[ \boxed{8\sqrt{2}} \]