Simplify and classify the result as rational or irrationa \( \sqrt{8} \)

To simplify and classify the expression \( \sqrt{8} \): ### **Simplification:** \[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} \] ### **Classification:** - **Rational or Irrational?** The number \( \sqrt{2} \) is **irrational**, meaning it cannot be expressed as a fraction of two integers. Multiplying an irrational number by a rational number (in this case, 2) results in an **irrational** number. Therefore, \( 2\sqrt{2} \) is **irrational**. ### **Final Answer:** \[ \sqrt{8} = 2\sqrt{2} \quad \text{(Irrational)} \]