Question
What is a rational number with a denominator of 7 that is between square root of 7 and square root of 8. Write your answer as an improper fraction
Answers
Answer
it says with a denominator of 7
Answered by
GPT 3.5
To find a rational number with a denominator of 7 that lies between √7 and √8, we can convert both square roots to fractions with a denominator of 7, and then average those fractions.
√7 ≈ 7/7 = 49/7
√8 ≈ 8/7
Taking the average of 49/7 and 8/7 gives us:
(49/7 + 8/7) / 2 = 57/14
Thus, a rational number with a denominator of 7 that lies between √7 and √8 is 57/14 (written as an improper fraction).
√7 ≈ 7/7 = 49/7
√8 ≈ 8/7
Taking the average of 49/7 and 8/7 gives us:
(49/7 + 8/7) / 2 = 57/14
Thus, a rational number with a denominator of 7 that lies between √7 and √8 is 57/14 (written as an improper fraction).
Answered by
GPT 3.5
Apologies for the misunderstanding. To find a rational number with a denominator of 7 that lies between √7 and √8, we can multiply both square roots by 7 to obtain fractions with a denominator of 7.
√7 * 7 = 7√7 ≈ 7(2.65) = 18.55 ≈ 19
√8 * 7 = 7√8 ≈ 7(2.83) = 19.81 ≈ 20
Thus, a rational number with a denominator of 7 that lies between √7 and √8 is 19/7 (written as an improper fraction).
√7 * 7 = 7√7 ≈ 7(2.65) = 18.55 ≈ 19
√8 * 7 = 7√8 ≈ 7(2.83) = 19.81 ≈ 20
Thus, a rational number with a denominator of 7 that lies between √7 and √8 is 19/7 (written as an improper fraction).
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