Question

simplifying radicals (with i)
digital scavenger hunt
start
√-60
-sqrt{-48}
2i√15
3i√15
-6√10
-4√10
14i√2
-27i√2
-14i√3
-4i√3
-5i√3
-9√3

Explanation:

Step1: Simplify \(\sqrt{-60}\)

Recall that \(\sqrt{-a}=i\sqrt{a}\) for \(a>0\). So, \(\sqrt{-60}=i\sqrt{60}\). Now, factor \(60\) into perfect squares and other factors: \(60 = 4\times15\), and \(\sqrt{4\times15}=\sqrt{4}\times\sqrt{15}=2\sqrt{15}\). Thus, \(\sqrt{-60}=i\times2\sqrt{15}=2i\sqrt{15}\).

Step2: Find the matching hexagon

Looking at the top row of hexagons, we see that \(2i\sqrt{15}\) is one of the hexagons (the second one from the left, green - colored? Wait, the green - like (or the second hexagon) has \(2i\sqrt{15}\). So we match \(\sqrt{-60}\) to \(2i\sqrt{15}\).

Answer:

The hexagon with \(2i\sqrt{15}\) (the second hexagon from the left in the top row) is the match for \(\sqrt{-60}\).