To find a rational number with a denominator of 7 between √7 and √8, we need to determine which number around √7 and √8 has a denominator of 7 when expressed as a fraction.
We can estimate that √7 is between 2 and 3, since 2^2 = 4 and 3^2 = 9.
We can estimate that √8 is between 2 and 3 as well since 2^2 = 4 and 3^2 = 9.
To find a number with a denominator of 7, we can try 7 divided by 2 and 7 divided by 3.
7/2 ≈ 3.5
7/3 ≈ 2.33
Since 2.33 is closer to √7 and has a denominator of 7, we can conclude that 7/3 is the rational number we are looking for.
Rewriting 7/3 as an improper fraction, we get:
7/3 = 2 and 1/3
Therefore, the rational number with a denominator of 7 that is between √7 and √8 is 2 1/3.
What is a rational number with a denominator of 7 that is between sqrt(7) and sqrt(8) Write your answer as an improper fraction.
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