using a number line, what whole number and rational number to the nearest half is √97 between?
√97 is between ? and ?
9 is wrong
To compare π (pi) and √8 using rational approximations, we can use the value 3.14 for π and find the nearest decimal approximation for √8.
Using a calculator, we find that √8 is approximately 2.83.
Thus, the inequality statement comparing π (approximately 3.14) and √8 (approximately 2.83) is:
π > √8
9.5 and 10
To find the whole number and rational number to the nearest half that √97 is between, we need to identify the two consecutive numbers on the number line that are closest to the square root of 97.
First, we find the whole number that is less than the square root of 97.
√97 is approximately 9.84. The whole number less than 9.84 is 9.
Next, we find the whole number that is greater than the square root of 97.
√97 is also less than 10. The whole number greater than 9.84 is 10.
Therefore, on the number line, √97 is between the whole numbers 9 and 10.
Now, let's find the rational number to the nearest half that √97 is between.
To find the rational number, we calculate the average of the two whole numbers:
(9 + 10) / 2 = 19 / 2 = 9.5
Therefore, √97 is between the whole number 9 and the rational number 9.5.
√97 is between 9 and 10.
Using rational approximations, what is inequality statement comparing √ 21 √ 17?
To compare √21 and √17 using rational approximations, we can find the nearest whole number for each square root.
√21 is approximately 4.58, which is closer to the whole number 5.
√17 is approximately 4.12, which is closer to the whole number 4.
Thus, the inequality statement comparing √21 and √17 is:
√17 < √21