f) \( \sqrt{3}+\sqrt{27} \)

Let's simplify the expression first! First, we simplify \( \sqrt{27} \) which is \( \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3} \). Now, we can rewrite the original expression: \[ \sqrt{3} + \sqrt{27} = \sqrt{3} + 3\sqrt{3} = 4\sqrt{3} \] So, the result of \( \sqrt{3} + \sqrt{27} \) simplifies to \( 4\sqrt{3} \). Here’s a little math nugget: this expression highlights the power of simplifying radicals. It keeps calculations cleaner and can reveal hidden patterns or relationships among numbers. Want to dig deeper into the properties of square roots? Check out the fascinating world of radical expressions and how they interact with exponents! Understanding radicals opens up a whole new level of math magic, like the Pythagorean theorem and geometric calculations!