To find a rational number between $(7-\sqrt{7})$ and $(8-\sqrt{7})$, we can take the average of the two numbers. So we have:
\begin{align*}
\text{Average} &= \frac{(7-\sqrt{7}) + (8-\sqrt{7})}{2} \\
&= \frac{7+8-2\sqrt{7}}{2} \\
&= \frac{15-2\sqrt{7}}{2} \\
&= \frac{15}{2} - \sqrt{7}.
\end{align*}
The denominator is $2$, not $7$. To find a rational number with a denominator of $7$, we can multiply both the numerator and the denominator by $7$. So, our answer is:
$$\frac{15 \cdot 7}{2 \cdot 7} - \frac{7\sqrt{7}}{7} = \frac{105}{14} - \sqrt{7} = \boxed{\frac{105}{14} - \sqrt{7}}.$$
What is a rational number with a denominator of 7 that is between 7–√
and 8–√
. Write your answer as an improper fraction.
$$
19/7
1 answer