d. \( 2 \sqrt{8} \times \sqrt{3} \)

To simplify \( 2 \sqrt{8} \times \sqrt{3} \), first simplify \( \sqrt{8} \) which is \( \sqrt{4 \times 2} = 2\sqrt{2} \). So, we have: \[ 2 \sqrt{8} \times \sqrt{3} = 2 \times 2\sqrt{2} \times \sqrt{3} = 4\sqrt{6}. \] Here, \( \sqrt{6} \) comes from multiplying \( \sqrt{2} \) and \( \sqrt{3} \). Next, did you know that simplifying square roots is also about breaking numbers down into their prime factors? This technique isn't just useful for even roots; it can be your handy tool for higher powers as well. For example, knowing \( 64 = 2^6 \) can help you quickly simplify \( \sqrt{64} \) to \( 8 \) without messing around with trial and error! If you’re interested in mastering these tricks, you might want to explore Khan Academy's resources on properties of square roots. They have engaging videos and interactive exercises that can really help solidify your understanding, making math feel less like a chore and more like a fun puzzle!