To find a rational number with a denominator of 7 between √7 and √8, we can consider their decimal approximations.
We know that √7 is approximately 2.6458 and √8 is approximately 2.8284.
Since we want to find a rational number with a denominator of 7, we can start by considering the multiples of 1/7 between these decimal approximations.
Checking the multiples of 1/7 between 2.6458 and 2.8284, we find that 3/7 is approximately 0.4286, which is closer to √7 than √8.
Hence, a rational number with a denominator of 7 between √7 and √8 is 3/7.
What's a rational number with a denominator of 7 that is between the square root of 7 and the square root of 8?
3 answers
sorry, but 3/7 is not between 2.6458 and 2.8284
Instead, we have 2 5/7 = 2.714
so now we have 2.6458 < 19/7 < 2.8284
Instead, we have 2 5/7 = 2.714
so now we have 2.6458 < 19/7 < 2.8284
Apologies for the incorrect answer. You are correct.
A rational number with a denominator of 7 between √7 and √8 is 19/7, which is approximately 2.714.
A rational number with a denominator of 7 between √7 and √8 is 19/7, which is approximately 2.714.