1. The problem asks to evaluate the expression $\sqrt{16c_6}$.\n\n2. First, let's interpret the notation. If $16c_6$ means the binomial coefficient $\binom{16}{6}$, then we calculate $\binom{16}{6}$ which is the number of ways to choose 6 objects out of 16.\n\n3. The formula for combinations is: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ where $n=16$ and $k=6$.\n\n4. Calculate factorials as needed: $$\binom{16}{6} = \frac{16!}{6! \cdot 10!}$$\n\n5. Simplify $\binom{16}{6}$ by expanding numerator and denominator partially: $$\binom{16}{6} = \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11}{6 \times 5 \times 4 \times 3 \times 2 \times 1}$$\n\n6. Compute numerator: $16 \times 15 = 240$, $240 \times 14 = 3360$, $3360 \times 13 = 43680$, $43680 \times 12 = 524160$, $524160 \times 11 = 5765760$.\n\n7. Compute denominator: $6 \times 5 = 30$, $30 \times 4 = 120$, $120 \times 3 = 360$, $360 \times 2 = 720$, $720 \times 1 = 720$.\n\n8. Divide numerator by denominator: $$\frac{5765760}{720} = 8008$$\n\n9. So, $\binom{16}{6} = 8008$. Now take the square root: $$\sqrt{8008}$$\n\n10. Approximate $\sqrt{8008}$. Since $89^2=7921$ and $90^2=8100$, $\sqrt{8008}$ is about $89.5$.\n\nTherefore, $\sqrt{\binom{16}{6}} \approx 89.5$.