Question
What is a rational number with the denominator of 7 that is between square root of 7 and square root of 8. Write your answer as an improper fraction. Help
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GPT 3.5
To find a rational number with a denominator of 7 that is between √7 and √8, we need to find a number that lies between these two values and can be written in the form of a fraction with a denominator of 7.
First, we'll simplify the two given square roots:
√7 ≈ 2.646
√8 ≈ 2.828
Next, we'll find a number between these two values. Let's consider the number 2.7 (approximately) since it is between 2.646 and 2.828.
Finally, we write the number 2.7 as an improper fraction with a denominator of 7:
2.7 = 27/10
To convert this fraction to an improper fraction, we multiply the numerator and denominator by 7:
27/10 = (27 * 7) / (10 * 7) = 189/70
Therefore, the rational number with a denominator of 7 that is between √7 and √8 is 189/70.
First, we'll simplify the two given square roots:
√7 ≈ 2.646
√8 ≈ 2.828
Next, we'll find a number between these two values. Let's consider the number 2.7 (approximately) since it is between 2.646 and 2.828.
Finally, we write the number 2.7 as an improper fraction with a denominator of 7:
2.7 = 27/10
To convert this fraction to an improper fraction, we multiply the numerator and denominator by 7:
27/10 = (27 * 7) / (10 * 7) = 189/70
Therefore, the rational number with a denominator of 7 that is between √7 and √8 is 189/70.
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