Question

match this irrational number with the best fractional estimate for it from the following choices.
\\(\sqrt{5}\\)
after you pick your answer press go.
a. \\(\frac{2}{3}\\) b. \\(\frac{56}{25}\\) c. \\(\frac{13}{8}\\)
d. \\(\frac{19}{3}\\) e. \\(\frac{6}{11}\\)

Explanation:

Step1: Calculate the value of $\sqrt{5}$

We know that $\sqrt{4} = 2$ and $\sqrt{9}=3$, so $\sqrt{5}$ is between 2 and 3. Let's calculate the approximate value of $\sqrt{5}\approx2.236$.

Step2: Calculate the value of each option

• Option A: $\frac{2}{3}\approx0.667$
• Option B: $\frac{56}{25} = 2.24$
• Option C: $\frac{13}{8}=1.625$
• Option D: $\frac{19}{3}\approx6.333$
• Option E: $\frac{6}{11}\approx0.545$

Step3: Compare the values

We compare the approximate value of $\sqrt{5}\approx2.236$ with the values of each option. We can see that $\frac{56}{25} = 2.24$ is the closest to $2.236$.

Answer:

B. $\frac{56}{25}$