what is a rational number that is between square root of 7 and the square root of 8 answer as improper fraction
To find a rational number between √7 and √8, we can first convert them into improper fractions.
√7 = √(7/1) = √7/√1 = √7/1
√8 = √(8/1) = √8/√1 = √8/1
Now, we need to find a fraction that lies between these two fractions.
Multiplying both the numerator and denominator of √7 by √1 (which is equivalent to 1) to rationalize the denominator, we have:
√7/1 = (√7/1) * (√1/√1) = √7 * √1 / 1 * √1 = (√7 * √1) / (√1 * √1) = √(7 * 1) / √(1 * 1) = √7 / 1 = √7
Similarly, multiplying both the numerator and denominator of √8 by √1 (which is equivalent to 1) to rationalize the denominator:
√8/1 = (√8/1) * (√1/√1) = √8 * √1 / 1 * √1 = (√8 * √1) / (√1 * √1) = √(8 * 1) / √(1 * 1) = √8 / 1 = √8
Therefore, the rational number between √7 and √8 can be written as the improper fraction:
√7/1 = √(7/1) = √7/1 = √7.
To find a rational number between √7 and √8, we need to make use of the fact that rational numbers can be expressed as fractions.
First, let's simplify the square roots:
√7 ≈ 2.646
√8 ≈ 2.828
Now, we need to find a fraction that falls between these two values.
Let's choose the fraction 9/4, which is equal to 2.25.
To check if this fraction falls between √7 and √8, we need to compare their decimal approximations:
2.646 < 2.25 < 2.828
Since 2.25 is between 2.646 and 2.828, it is a rational number between √7 and √8 in its improper fraction form of 9/4.