Question

Find a rational number with one decimal place that is between 17−−√ and 18−−√ .

Answer 1

To find a rational number between $\sqrt{17}$ and $\sqrt{18}$, we can take the average of the two numbers. The average is \begin{align*}
\frac{(\sqrt{17}) + (\sqrt{18})}{2} &= \frac{(\sqrt{17}) + (\sqrt{18})}{2}\cdot \frac{(\sqrt{17}) - (\sqrt{18})}{(\sqrt{17}) - (\sqrt{18})}\\
&=\frac{17+18}{2(\sqrt{17})+\sqrt{18}}\\
&= \frac{35}{2\sqrt{17}+\sqrt{18}}\cdot\frac{\sqrt{18}-\sqrt{17}}{\sqrt{18}-\sqrt{17}\\
&= \frac{35(\sqrt{18}-\sqrt{17})}{2(\sqrt{17})^2 + 2\sqrt{17}\sqrt{18} + (\sqrt{18})^2-(\sqrt{17})^2}\\
&= \frac{(35)(\sqrt{18}-\sqrt{17})}{(\sqrt{18})^2 -(\sqrt{17})^2}\\
&=\frac{(35)(\sqrt{18}-\sqrt{17})}{18-17}\\
&= (35)(\sqrt{18}-\sqrt{17}).
\end{align*}Since $4^2 = 16$ and $5^2 = 25$, we know $16 < 17 < 18 < 25$, and squaring each of these numbers yields $256 < 289 < 324$. So a number between $\sqrt{17}$ and $\sqrt{18}$ is $(35)(4-5)=\boxed{-35}$.

Answer 2

bro what

Answer 3

wtf is that bs LOL

Answer 4

Better do it yourself! This so Called "Robot" gives very different answers and sometimes random.

Answer 5

that- is a very interesting answer xDDDD

Answer 6

bro really just gave out his program

Answer 7

the answer is 4.2

Answer 8

4.2 is right