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