(3) \( \sqrt{\sqrt[3]{8}} \)

To solve \( \sqrt{\sqrt[3]{8}} \), let's begin by simplifying inside out. The cube root of 8 can be expressed as \( \sqrt[3]{8} = 2 \) since \( 2^3 = 8 \). Now, applying the square root to this result gives us \( \sqrt{2} \). Ultimately, the simplified expression is \( \sqrt{2} \). For an extra bit of fun, you might be interested to know that the value of \( \sqrt{2} \) is approximately 1.414. It’s famous in mathematics and is often used in geometry, especially when it comes to calculating the diagonal of a square with unit sides—it’s essentially the golden number of right triangles! Additionally, you can explore the theme of surds—irrational numbers like \( \sqrt{2} \). They pop up in various areas like trigonometry and calculus, providing deeper insights into geometry and algebra. Dive into those textbooks or online resources, and you’ll find loads of fascinating applications!