Question

is square root of 8 plus square root of 2 is irrational or rational

Answer 1

To determine whether \( \sqrt{8} + \sqrt{2} \) is rational or irrational, let's simplify it.

First, we can express \( \sqrt{8} \):

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

Now we can write the expression:

\[
\sqrt{8} + \sqrt{2} = 2\sqrt{2} + \sqrt{2} = 3\sqrt{2}
\]

Next, we need to determine if \( 3\sqrt{2} \) is rational or irrational. We know that \( \sqrt{2} \) is an irrational number. When you multiply an irrational number (like \( \sqrt{2} \)) by a non-zero rational number (like \( 3 \)), the result is still irrational.

Therefore, \( 3\sqrt{2} \) is irrational, which means that:

\[
\sqrt{8} + \sqrt{2} \text{ is irrational.}
\]