Question

match this irrational number with the best fractional estimate for it from the following choices.\\(\sqrt{14}\\)\
after you pick your answer press go.\
a. \\(\frac{2}{13}\\)\
b. \\(\frac{17}{2}\\)\
c. \\(\frac{1}{15}\\)\
d. \\(\frac{15}{4}\\)\
e. \\(\frac{19}{5}\\)

Explanation:

Step1: Calculate the value of \(\sqrt{14}\)

We know that \(3^2 = 9\) and \(4^2=16\), so \(\sqrt{14}\) is between \(3\) and \(4\), and closer to \(4\) since \(14\) is closer to \(16\) than to \(9\). \(\sqrt{14}\approx 3.7417\)

Step2: Calculate the value of each option

• Option A: \(\frac{2}{13}\approx0.1538\)
• Option B: \(\frac{17}{2} = 8.5\)
• Option C: \(\frac{1}{15}\approx0.0667\)
• Option D: \(\frac{15}{4}=3.75\)
• Option E: \(\frac{19}{5} = 3.8\)

Step3: Compare the values

We compare the approximate value of \(\sqrt{14}\approx3.7417\) with the values of each option. The value of option D (\(3.75\)) is the closest to \(3.7417\)

Answer:

D. \(\frac{15}{4}\)