Using a number line, what whole number and rational number to the nearest half is 40−−√ between? (1 point)
To represent the whole number and rational number closest to 58−√ on a number line, we need to find the values of 58−√ that are right before and right after it.
The approximate value of 58−√ can be found by calculating the square root of 58. Using a calculator, the square root of 58 is approximately 7.6157.
For the whole number that is right before 58−√, we round down the value of 7.6157 to the nearest whole number, which is 7.
For the whole number that is right after 58−√, we round up the value of 7.6157 to the nearest whole number, which is 8.
On the number line, we can represent this as:
... 6.5, 7, 7.5, 8, ...
To find the rational number closest to 58−√, we need to determine whether 58−√ is closer to 7 or 8 on the number line.
The distance between 58−√ and 7 is 58−√ − 7 ≈ 0.6157.
The distance between 58−√ and 8 is 58−√ − 8 ≈ -0.3843.
Since the distance is smaller when comparing to 7, this means that the rational number closest to 58−√ is 7.5.
Therefore, the whole number and rational number closest to 58−√ on the number line are 7 and 7.5, respectively.
To represent the whole number and rational number closest to 40−√ on a number line, we need to find the values of 40−√ that are right before and right after it.
First, let's find the whole number that is closest to 40−√. We can start by finding the square root of 40, which is approximately 6.32. So, 40−√ is between 6 and 7. We can represent this on the number line:
... 5.5, 6, 6.5, 7, ...
Next, let's find the rational number that is closest to 40−√. One way to do this is to determine the distance between 40−√ and both 6 and 7.
The distance between 40−√ and 6 is 40−√ − 6 ≈ 0.32.
The distance between 40−√ and 7 is 40−√ − 7 ≈ -0.68.
Since the distance is smaller when comparing to 6, this means that the rational number closest to 40−√ is 6.5.
Therefore, the whole number and rational number closest to 40−√ on the number line are 6 and 6.5, respectively.
Wrong
Apologies for the confusion. Let's correct the answer.
To represent the whole number and rational number closest to √40 on a number line, we need to find the values of √40 that are right before and right after it.
The approximate value of √40 is about 6.32.
The whole number that is right before √40 is 6, and the whole number that is right after √40 is 7.
The rational number that is right before √40 is the whole number 6, and the rational number that is right after √40 is the whole number 7.
Therefore, the whole number and rational number closest to √40 on the number line are 6 and 7, respectively.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?
Using rational approximations, what is an inequality statement comparing √81 and √88?
Let's approximate the values of √81 and √88 using rational approximations.
The square root of 81 is an exact value and equals 9.
To approximate the square root of 88, we can find the two perfect squares that it falls between: 81 and 100.
√81 = 9
√100 = 10
Since 88 falls between 81 and 100, its square root is between 9 and 10.
Using these approximations, we can write the inequality statement as:
9 < √88 < 10
Yes but is it greater than, less than or equal to?
Apologies for not clarifying that in the initial response. To determine the relationship between √81 and √88, we compare their values.
We have:
√81 = 9
√88 ≈ 9.38
Since 9.38 is greater than 9, we can write the inequality statement as:
√81 < √88
To solve this problem, we need to find a whole number and a rational number that are closest to the square root of 40.
First, we need to find the whole number between which the square root of 40 lies on the number line. We know that the square root of 36 is 6, and the square root of 49 is 7. Since the square root of 40 is between these two numbers, we can conclude that the whole number closest to the square root of 40 is 6.
Next, we need to find a rational number to the nearest half. To do this, we can take the average of the two whole numbers on either side of the square root of 40. In this case, the whole numbers on either side are 6 and 7. The average of these two numbers is (6 + 7) / 2 = 6.5. Thus, 6.5 is the rational number closest to the square root of 40 to the nearest half.
Therefore, the whole number closest to the square root of 40 is 6, and the rational number to the nearest half is 6.5.