what rational number to the nearest half is 97−−√
To determine the rational number to the nearest half for √97, we need to find the two nearest perfect squares. The perfect squares closest to 97 are 81 (9^2) and 100 (10^2).
The difference between 97 and 81 is 16, while the difference between 100 and 97 is also 16. Since 97 is closer to 100, we can assume √97 is closer to 10 than to 9.
Therefore, the rational number to the nearest half for √97 is 10.
what is the whole and rational number of √97
The whole number closest to √97 is 9 because 9^2 = 81, which is the largest perfect square less than 97.
To find the rational number closest to √97, we can express √97 as a fraction. Since 97 is not a perfect square, √97 is an irrational number.
Hence, the whole number closest to √97 is 9, and there is no rational number equivalent to √97.
Using a number line, what whole number and rational number to the nearest half is 97−−√ between?(1 point)
To determine the whole number and rational number to the nearest half for √97, we can place it on a number line.
Let's consider the numbers around √97 on a number line:
9 9.5 10
Since √97 is between 9 and 10, the whole number to the nearest half is 9.5. However, since √97 is an irrational number, there is no rational number equivalent to √97.
Therefore, the whole number to the nearest half for √97 is 9.5, but there is no rational number equivalent to √97.
Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =.(1 point)
The inequality is: 21−−√
17−−√.
To compare 21−−√ and 17−−√ using rational approximations, we can find the rational numbers that are close to each of them.
For 21−−√, we know that √16 = 4 and √25 = 5. Therefore, we can approximate 21−−√ to be between 4 and 5.
For 17−−√, we know that √16 = 4 and √25 = 5. Therefore, we can approximate 17−−√ to also be between 4 and 5.
Since both approximations fall within the same range, we can conclude that 21−−√ is equal to 17−−√.
The inequality statement comparing 21−−√ and 17−−√ is: 21−−√ = 17−−√.
Using a number line, what is the approximate value of 19−−√?(1 point)
Responses
4.38
4.38
4.13
4.13
4.25
4.25
4.5
To approximate the value of √19 using a number line, we can look for the two perfect squares that 19 falls between:
4^2 = 16 and 5^2 = 25.
On a number line, we have:
4 4.25 4.5 4.75 5
Since 19 falls closer to 4.25 than to 4.5, we can estimate that √19 is approximately 4.25.
Therefore, the approximate value of 19−−√ is 4.25.
Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
Responses
between 9.5 and 10
between 9.5 and 10
between 10.5 and 11
between 10.5 and 11
between 11 and 11.5
between 11 and 11.5
between 10 and 10.5
To determine the whole number and rational number to the nearest half for √105, we can place it on a number line.
Let's consider the numbers around √105 on a number line:
9 9.5 10 10.5 11
Since √105 is between 10 and 10.5, the whole number to the nearest half is 10.5.
Therefore, the whole number to the nearest half for √105 is 10.5.
Using rational approximations, what statement is true?(1 point)
Responses
48−−√>36−−√
start root 48 end root greater than start root 36 end root
48−−√<36−−√
start root 48 end root less than start root 36 end root
49−−√>7
start root 49 end root greater than 7
49−−√<7
To compare 48−−√ and 36−−√ using rational approximations, we can find the rational numbers that are close to each of them.
For √48, we know that √49 = 7 and √64 = 8. Therefore, we can approximate √48 to be between 7 and 8.
For √36, we know that √36 = 6. Therefore, √36 is equal to 6.
Since √48 is greater than √36, the statement that is true is:
48−−√ > 36−−√.
Question
Using rational approximations, what statement is true?(1 point)
Responses
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
81−−√>9
start root 81 end root greater than 9
81−−√<9
start root 81 end root less than 9
71−−√>61−−√
To compare 71−−√ and 61−−√ using rational approximations, we can find the rational numbers that are close to each of them.
For √71, we know that √64 = 8 and √81 = 9. Therefore, we can approximate √71 to be between 8 and 9.
For √61, we know that √49 = 7 and √64 = 8. Therefore, we can approximate √61 to be between 7 and 8.
Since √71 is greater than √61, the statement that is true is:
71−−√ > 61−−√.