To find a rational number between two given irrational numbers, we need to find a rational number whose square falls between the squares of the given irrational numbers.
First, we square both the given irrational numbers:
(√7)^2 = 7
(√8)^2 = 8
We can see that 7 < 7.5^2 < 8, so we need to find a rational number whose square is 7.5^2.
To simplify the square, we note that 7.5 is half of 15, so 7.5^2 = (15/2)^2 = 15^2 / 2^2 = 225/4.
Therefore, a rational number with a denominator of 7 that is between √7 and √8 is:
225/4 ÷ 7 = 225/28.
So, the answer is 225/28.
What is a rational number with a denominator of 7 that is between √7 and √8 Write your answer as an improper fraction.
2 answers
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.(4 points)
1 answer