To find a rational number with a denominator of 7 between √7 and √8, we need to determine the two consecutive square roots between which the rational number will fall.
√7 is approximately 2.65, while √8 is approximately 2.83.
The rational number needs to be between these two values, so it must be greater than 2.65 but less than 2.83.
To express the rational number as an improper fraction, we can convert each square root to a fraction with a denominator of 7.
√7 ≈ 2.65 can be written as 2 65/100, which simplifies to 2 13/20 when we divide both the numerator and denominator by 5.
√8 ≈ 2.83 can be written as 2 83/100, which does not simplify any further.
Therefore, a rational number with a denominator of 7 that is between √7 and √8 is 2 14/20, which simplifies to 2 7/10.
What is a rational number with a denominator of 7 that is between √7 and √8. write your answer as an improper fraction.
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