QuestionApproximate $\sqrt{37}$ using perfect squares, referencing $\sqrt{36}=6$ and $\sqrt{49}=7$.

Studdy Solution
Calculate the rational approximation of $\sqrt{37}$.
$$\sqrt{37} \approx \frac{12}{13} \cdot6 + \frac{1}{13} \cdot7 = \frac{72}{13} + \frac{7}{13} = \frac{79}{13} =6.07692308$$So, the rational approximation of $\sqrt{37}$ using perfect squares is approximately6.08.