To find a rational number between 7–√ and 8–√ with a denominator of 7, we can first find the average of the two numbers:
(7-√ + 8-√) / 2
Simplifying this expression, we get:
(15 - 2√) / 2
Dividing both numerator and denominator by 2, we have:
15/2 - √2
To write this as an improper fraction, we multiply both the numerator and the denominator by 2:
(15/2 - √2) * 2/2
This gives us:
30/4 - 2√2/2
Simplifying further, we have:
15/2 - √2
What is a rational number with a denominator of 7 that is between 7–√
and 8–√. Write your answer as an improper fraction.(1 point)
7 answers
What is a rational number with a denominator of 7 that is between 7–√
and 8–√
and 8–√
To find a rational number between 7–√ and 8–√ with a denominator of 7, we need to find a rational number that is between the two given numbers.
The given numbers are 7–√ and 8–√.
To find a number between them, we can first try to simplify the given numbers.
7–√ can be rewritten as 7–√ / 1.
8–√ can be rewritten as 8–√ / 1.
To rationalize the denominators, we multiply each fraction by its conjugate:
(7–√ / 1) * (√+7 / √+7) gives us (7√+49-√^2 / 1), which simplifies to (7√+49-1)
(8–√ / 1) * (√+8 / √+8) gives us (8√+64-√^2 / 1), which simplifies to (8√+64-1)
Now we have simplified numbers, we need to find a rational number between them with a denominator of 7.
We can start by finding the average of the two numbers:
((7√+49-1) + (8√+64-1)) / 2
This simplifies to:
(7√+56 + 8√+63) / 2
Combining like terms:
(15√+119) / 2
To write this as an improper fraction, we multiply both the numerator and the denominator by 2:
(15√+119) * 2 / 2
This gives us:
30√+238 / 4
Simplifying further, we have:
15√+119 / 2
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 15√+119 / 2.
The given numbers are 7–√ and 8–√.
To find a number between them, we can first try to simplify the given numbers.
7–√ can be rewritten as 7–√ / 1.
8–√ can be rewritten as 8–√ / 1.
To rationalize the denominators, we multiply each fraction by its conjugate:
(7–√ / 1) * (√+7 / √+7) gives us (7√+49-√^2 / 1), which simplifies to (7√+49-1)
(8–√ / 1) * (√+8 / √+8) gives us (8√+64-√^2 / 1), which simplifies to (8√+64-1)
Now we have simplified numbers, we need to find a rational number between them with a denominator of 7.
We can start by finding the average of the two numbers:
((7√+49-1) + (8√+64-1)) / 2
This simplifies to:
(7√+56 + 8√+63) / 2
Combining like terms:
(15√+119) / 2
To write this as an improper fraction, we multiply both the numerator and the denominator by 2:
(15√+119) * 2 / 2
This gives us:
30√+238 / 4
Simplifying further, we have:
15√+119 / 2
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 15√+119 / 2.
but the answer has to be an improper fraction
I apologize for the mistake. Let's correct it.
To find a rational number between 7–√ and 8–√ with a denominator of 7, we need to find a number between them by calculating the average.
The given numbers are 7–√ and 8–√.
To find the average, we add the two numbers and divide by 2:
[(7–√) + (8–√)] / 2 = (15–2√) / 2 = 15/2 – √2
To write this as an improper fraction, we multiply the numerator and denominator by 2:
[(15/2 – √2) * 2] / 2 = (15 – 2√2) / 2 = 15/2 – √2
Therefore, the rational number with a denominator of 7 that is between 7–√ and 8–√ is 15/2 – √2.
To find a rational number between 7–√ and 8–√ with a denominator of 7, we need to find a number between them by calculating the average.
The given numbers are 7–√ and 8–√.
To find the average, we add the two numbers and divide by 2:
[(7–√) + (8–√)] / 2 = (15–2√) / 2 = 15/2 – √2
To write this as an improper fraction, we multiply the numerator and denominator by 2:
[(15/2 – √2) * 2] / 2 = (15 – 2√2) / 2 = 15/2 – √2
Therefore, the rational number with a denominator of 7 that is between 7–√ and 8–√ is 15/2 – √2.
NO NO AND NO!!
I apologize for the previous incorrect responses. Let's try again.
To find a rational number with a denominator of 7 that is between 7–√ and 8–√, we first need to find the decimal values of these two numbers.
7–√ ≈ 4.071
8–√ ≈ 3.928
Now, we need to find a rational number with a denominator of 7 that is between 4.071 and 3.928.
Let's find the average of these two decimal values:
(4.071 + 3.928) / 2 ≈ 3.9995
To write this as an improper fraction, we multiply both the numerator and denominator by 10000:
(39995 / 10000)
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 39995/10000.
To find a rational number with a denominator of 7 that is between 7–√ and 8–√, we first need to find the decimal values of these two numbers.
7–√ ≈ 4.071
8–√ ≈ 3.928
Now, we need to find a rational number with a denominator of 7 that is between 4.071 and 3.928.
Let's find the average of these two decimal values:
(4.071 + 3.928) / 2 ≈ 3.9995
To write this as an improper fraction, we multiply both the numerator and denominator by 10000:
(39995 / 10000)
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 39995/10000.
1 answer