1. Problem 1: Find $\sqrt{11001_2}$ and express the answer in base two.\n\n2. First, convert $11001_2$ (binary) to decimal:\n$$11001_2 = 1\times 2^4 + 1\times 2^3 + 0\times 2^2 + 0\times 2^1 + 1\times 2^0 = 16 + 8 + 0 + 0 + 1 = 25_{10}$$\n\n3. Now find $\sqrt{25}$ in decimal:\n$$\sqrt{25} = 5$$\n\n4. Convert $5_{10}$ back to binary:\n$$5_{10} = 101_2$$\n\n5. Hence, $\sqrt{11001_2} = 101_2$.\n\n---\n\n1. Problem 2: In a circle with tangent $PT$ at $T$, given $\angle ABT=35^\circ$ and $\angle CTP=42^\circ$, find $\angle ATC$.\n\n2. Recall that $PT$ is tangent at $T$, so $\angle CTP$ is between the tangent and the chord $CT$. The angle between tangent and chord equals the angle in the alternate segment. Thus,\n$$\angle CTP = \angle ATC = 42^\circ$$\n\n3. Therefore, the measure of $\angle ATC$ is $42^\circ$.