Question

what integer is between \\(\sqrt{7}\\) and \\(\frac{6\pi}{5}\\)?

Explanation:

Step1: Estimate $\sqrt{7}$

We know that $2^2 = 4$ and $3^2 = 9$. Since $4<7<9$, we have $2<\sqrt{7}<3$. More precisely, $\sqrt{7}\approx2.6458$.

Step2: Estimate $\frac{6\pi}{5}$

We know that $\pi\approx3.1416$, so $\frac{6\pi}{5}=\frac{6\times3.1416}{5}=\frac{18.8496}{5} = 3.76992$.

Step3: Find the integer between them

We need an integer $n$ such that $\sqrt{7}

Answer:

3