Question

match this irrational number with the best fractional estimate for it from the following choices.
\\(\sqrt{3}\\)
after you pick your answer press go.
a. \\(\frac{17}{10}\\) b. \\(\frac{8}{7}\\) c. \\(\frac{9}{2}\\)
d. \\(\frac{8}{19}\\) e. \\(\frac{10}{17}\\)

Explanation:

Step1: Calculate the approximate value of $\sqrt{3}$

We know that $\sqrt{3}\approx1.732$.

Step2: Calculate the value of each option

• Option A: $\frac{17}{10} = 1.7$
• Option B: $\frac{8}{7}\approx1.143$
• Option C: $\frac{9}{2}=4.5$
• Option D: $\frac{8}{19}\approx0.421$
• Option E: $\frac{10}{17}\approx0.588$

Step3: Compare the values

We compare the approximate value of $\sqrt{3}$ (≈1.732) with the values of each option. The value of option A ($1.7$) is closest to $1.732$ among all the options.

Answer:

A. $\frac{17}{10}$