Using a number line, what whole number and rational number to the nearest half is 68−−√
between?(1 point)
Responses
between 9 and 9.5
between 9 and 9.5
between 8.5 and 9
between 8.5 and 9
between 7.5 and 8
between 7.5 and 8
between 8 and 8.5
between 8 and 8.5
Using rational approximations, what is an inequality statement comparing 91−−√
and 98−−√
? Enter <, >, or =.(1 point)
The inequality is: 91−−√
98−−√
The inequality is: 91−−√ < 98−−√
To determine the whole number and rational number to the nearest half that 68−−√ is between, we can use a number line.
First, let's find the whole number portion of 68−−√. The square root of 68 is approximately 8.246.
Next, let's find the rational number portion of 68−−√ to the nearest half. Since the square root of 68 is closer to 8 than 9, we can say that 68−−√ is closer to 8 than 9. To find the midpoint between 8 and 9, we add the two numbers and divide by 2.
(8 + 9) / 2 = 17 / 2 = 8.5
Therefore, 68−−√ is between the whole number 8 and the rational number 8.5 on the number line.
Thus, the correct answer is: between 8 and 8.5