Question

What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction

Answer 1

To find a rational number between $7-\sqrt7$ and $8-\sqrt7$, we can take their average. The average of two numbers is the sum of the two numbers divided by 2, so $\frac{(7-\sqrt7)+(8-\sqrt7)}{2}=\frac{15-2\sqrt7}{2}=\frac{15}{2}-\frac{2\sqrt7}{2}=\frac{15}{2}-\sqrt7$. Simplifying, we have $$\frac{15}{2}-\sqrt7=\boxed{\frac{15-2\sqrt7}{2}}.$$