In the square root spiral, the first triangle has two sides of 1, and each new triangle has one…

Step 1. The rule. After $n$ triangles the long side is $\sqrt{n + 1}$.

Step 2. Longer than 3. $n + 1 > 9$. At $n = 8$ the side is exactly $\sqrt{9} = 3$, which is not longer. So $n = 9$, with $\sqrt{10} \approx 3.162$.

Step 3. Longer than 5. $n + 1 > 25$, so $n = 25$, with $\sqrt{26} \approx 5.099$.