Add two square root root of 8+3 square root of eight

1 answer

To simplify the expression \(2\sqrt{8} + 3\sqrt{8}\), we can start by combining the terms since they both have the same radical part \(\sqrt{8}\).

First, factor out \(\sqrt{8}\):

\[ 2\sqrt{8} + 3\sqrt{8} = (2 + 3)\sqrt{8} = 5\sqrt{8} \]

Next, we can simplify \(\sqrt{8}\):

\[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \]

Now, substitute \( \sqrt{8} \) back into the expression:

\[ 5\sqrt{8} = 5(2\sqrt{2}) = 10\sqrt{2} \]

So, the simplified form of \(2\sqrt{8} + 3\sqrt{8}\) is:

\[ 10\sqrt{2} \]