Which of the following is closest to $\sqrt{3}$?

### Concept & Value The square root of $3$ ($\sqrt{3}$) is an irrational number with a well-known approximate value: $$\sqrt{3} \approx 1.73205$$ ### Step-by-Step Solution * **Given:** Options representing approximations of $\sqrt{3}$. * **Calculation:** Convert all options to decimal form to compare with $1.73205$: * (a) $1.69$ * (b) $\frac{173}{100} = 1.73$ * (c) $1.75$ * (d) $\frac{9}{5} = 1.8$ Calculate the absolute differences: * $|1.73205 - 1.69| = 0.04205$ * $|1.73205 - 1.73| = 0.00205$ * $|1.73205 - 1.75| = 0.01795$ * $|1.73205 - 1.8| = 0.06795$ The smallest difference is $0.00205$, corresponding to $1.73$. ### Exam Strategy & Shortcut Memorizing basic radical values saves significant time. $\sqrt{2} \approx 1.414$ and $\sqrt{3} \approx 1.732$. Knowing $\sqrt{3} \approx 1.732$ lets you immediately match it to $1.73$, which is precisely $\frac{173}{100}$. ### Common Pitfall * **Mistake:** Rounding up prematurely to $1.75$ or confusing $\frac{9}{5}$ ($1.8$) with a closer approximation. * **Tip:** Always write down the value of standard constants up to 3 decimal places to avoid proximity errors. ### Final Answer **Therefore, the correct answer is 173/100.**