Find a rational number with one decimal place that is between 17−−√ and 18−−√
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To find a rational number between $\sqrt{17}$ and $\sqrt{18}$, we can "rationalize" the denominator. To do this, we multiply the numerator and denominator of $\frac{1}{\sqrt{17}}$ by $\sqrt{17}$ to get \begin{align*}
\frac{1}{\sqrt{17}} &= \frac{1}{\sqrt{17}}\cdot \frac{\sqrt{17}}{\sqrt{17}}\\
&= \frac{\sqrt{17}}{17}.
\end{align*} Similarly, to rationalize the denominator of $\frac{1}{\sqrt{18}}$, we multiply the numerator and denominator of $\frac{1}{\sqrt{18}}$ by $\sqrt{18}$ to get \begin{align*}
\frac{1}{\sqrt{18}} &= \frac{1}{\sqrt{18}}\cdot \frac{\sqrt{18}}{\sqrt{18}}\\
&= \frac{\sqrt{18}}{18}\\
&= \frac{3\sqrt{2}}{18}\\
&= \frac{\sqrt{2}}{6}.
\end{align*} Therefore, the rational number between $\sqrt{17}$ and $\sqrt{18}$ is $\boxed{\dfrac{\sqrt{17}}{17}}$.
Find a rational number with one decimal place that is between 17−−√ and 18−−√
To find a rational number between $\sqrt{17}$ and $\sqrt{18}$, we can find the average of these two numbers. Since $\sqrt{17} \approx 4.1$ and $\sqrt{18} \approx 4.2,$ the average is $\frac{4.1+4.2}{2} = 4.15,$ which is a decimal number with one decimal place. Therefore, a rational number with one decimal place that is between $\sqrt{17}$ and $\sqrt{18}$ is $\boxed{4.2}.$
Which of the following is between π and 11−−√?(1 point)
To determine which number is between $\pi$ and $\sqrt{11},$ we can find their average. Since $\pi \approx 3.14$ and $\sqrt{11} \approx 3.32,$ the average is $\frac{3.14+3.32}{2} = 3.23.$ Therefore, the number $3.23$ is between $\pi$ and $\sqrt{11}.$ Thus, the answer is $\boxed{3.23}.$
Which of the following is between π and 11−−√?(1 point)
10−−√
12−−√
7–√
8–√