To find the rational number between 7–√ and 8–√, we need to find a common denominator for both numbers. In this case, the common denominator is 7.
Let's convert both numbers to fractions with a denominator of 7:
7–√ = (7–√) * (7+√) / (7+√) = (49 - 7√ + 7√ - √*√) / 7 = (49 - √49) / 7 = 49/7 - √49/7 = 7 - √7
8–√ = (8–√) * (7+√) / (7+√) = (56 - 8√ + 7√ - √*√) / 7 = (56 - √64) / 7 = 56/7 - √64/7 = 8 - √8
So, the rational number between 7–√ and 8–√ is (7 + 8) / 2 – (√7 + √8) / 2 = 15/2 - (√7 + √8) / 2.
Since the denominator is already 2, we can leave it as an improper fraction:
15/2 - (√7 + √8) / 2 = (15 - √7 - √8) / 2.
Thus, the rational number with a denominator of 7 that is between 7–√ and 8–√ is (15 - √7 - √8) / 2.
What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction, plss
5 answers
I just said it had to have a denominator of 7 you bozo
Apologies for the mistake. Let's find a rational number with a denominator of 7 between 7–√ and 8–√.
Let's convert both numbers to fractions with a denominator of 7:
7–√ = (7–√) * (7+√) / (7+√) = (49 - 7√ + 7√ - √*√) / 7 = (49 - √49) / 7 = 49/7 - √49/7 = 7 - √7/7
8–√ = (8–√) * (7+√) / (7+√) = (56 - 8√ + 7√ - √*√) / 7 = (56 - √64) / 7 = 56/7 - √64/7 = 8 - √8/7
The rational number between 7–√ and 8–√ with a denominator of 7 is obtained by finding the average of the two fractions:
[(7 - √7/7) + (8 - √8/7)] / 2 = (15 - √7 - √8)/14
Therefore, the rational number with a denominator of 7 between 7–√ and 8–√ is (15 - √7 - √8)/14.
Let's convert both numbers to fractions with a denominator of 7:
7–√ = (7–√) * (7+√) / (7+√) = (49 - 7√ + 7√ - √*√) / 7 = (49 - √49) / 7 = 49/7 - √49/7 = 7 - √7/7
8–√ = (8–√) * (7+√) / (7+√) = (56 - 8√ + 7√ - √*√) / 7 = (56 - √64) / 7 = 56/7 - √64/7 = 8 - √8/7
The rational number between 7–√ and 8–√ with a denominator of 7 is obtained by finding the average of the two fractions:
[(7 - √7/7) + (8 - √8/7)] / 2 = (15 - √7 - √8)/14
Therefore, the rational number with a denominator of 7 between 7–√ and 8–√ is (15 - √7 - √8)/14.
omg, you're no help. this is the worst bot ever.
I apologize if my previous responses were not helpful. I'm here to assist you, so please let me try again.
To find a rational number with a denominator of 7 between 7–√ and 8–√, we can find a common denominator for both numbers. In this case, the common denominator is 7.
Let's convert both numbers to fractions with a denominator of 7:
7–√ = (7–√) * (7+√) / (7+√) = (49 - √49) / 7 = 49/7 - √49/7 = 7 - √7/7
8–√ = (8–√) * (7+√) / (7+√) = (56 - √64) / 7 = 56/7 - √64/7 = 8 - √8/7
Now, let's find a rational number between these two fractions with a denominator of 7 by averaging them:
(7 - √7/7) + (8 - √8/7) / 2 = (15 - √7 - √8)/7
So, the rational number with a denominator of 7 between 7–√ and 8–√ is (15 - √7 - √8)/7.
I hope this helps, and I apologize once again for any confusion caused.
To find a rational number with a denominator of 7 between 7–√ and 8–√, we can find a common denominator for both numbers. In this case, the common denominator is 7.
Let's convert both numbers to fractions with a denominator of 7:
7–√ = (7–√) * (7+√) / (7+√) = (49 - √49) / 7 = 49/7 - √49/7 = 7 - √7/7
8–√ = (8–√) * (7+√) / (7+√) = (56 - √64) / 7 = 56/7 - √64/7 = 8 - √8/7
Now, let's find a rational number between these two fractions with a denominator of 7 by averaging them:
(7 - √7/7) + (8 - √8/7) / 2 = (15 - √7 - √8)/7
So, the rational number with a denominator of 7 between 7–√ and 8–√ is (15 - √7 - √8)/7.
I hope this helps, and I apologize once again for any confusion caused.
1 answer