how is 19/7 an improper fraction in between the square root of 7 and the square root of 8
To determine if 19/7 is an improper fraction between √7 and √8, we need to compare its value to the values of √7 and √8.
First, let's calculate the values of √7 and √8 using a calculator:
√7 ≈ 2.65
√8 ≈ 2.83
Now, let's convert 19/7 into a decimal:
19 ÷ 7 ≈ 2.71
Comparing the value of 19/7 (2.71) to the values of √7 (2.65) and √8 (2.83), we can conclude that 19/7 does not fall between the square roots of 7 and 8.
To determine if 19/7 is an improper fraction between the square root of 7 (√7) and the square root of 8 (√8), we need to compare the decimal values of these numbers.
First, let's calculate the decimal value of 19/7:
19 ÷ 7 = 2.71428571429 (rounded to 11 decimal places)
Next, let's find the decimal values of √7 and √8:
√7 = 2.64575131 (rounded to 8 decimal places)
√8 = 2.82842712 (rounded to 8 decimal places)
As we can see, the decimal value of 19/7 is greater than the decimal value of √7 (2.64575131) and smaller than the decimal value of √8 (2.82842712). Therefore, 19/7 is indeed an improper fraction between √7 and √8.