Using rational approximations, what statement is true?(1 point)
81−−√<9
71−−√>61−−√
81−−√>9
71 −−−√<61−−√
81−−√ > 9
Using rational approximations, what statement is true?
49−−√<7
48−−√>36−−√
49−−√>7
48−−√<36−−√
49−−√<7
Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?
between 10 and 10.5
between 10.5 and 11
between 9.5 and 10
between 11 and 11.5
Between 10 and 10.5
Using a number line, what is the approximate value of 19−−√?
4.5
4.25
4.38
4.13
The approximate value of 19−−√ is 4.38.
Using rational approximations, what statement is true?
16−−√>4
16 −−−√<4
12 −−−√<π
12 −−−√>π
16−−√ > 4
To compare rational approximations, we can convert the given square root expressions into rational numbers. Let's simplify each expression:
1) Simplifying √81:
√81 = √(9 * 9) = 9
2) Simplifying √71:
To find a rational approximation for √71, we need to find two perfect squares that are closest to 71. Since √64 = 8 and √81 = 9, we can estimate that √71 is between 8 and 9. Let's consider the midpoint:
√71 is closer to √64 than √81, so we can approximate it as 8.4.
3) Simplifying √61:
Similarly, we need to find two perfect squares close to 61. We have √49 = 7 and √64 = 8. Since √61 is closer to √64 than √49, we can approximate it as 8.
Now, let's compare the rational approximations:
1) 81−−√ < 9
This is false because √81 equals exactly 9, so it is not less.
2) 71−−√ > 61−−√
This is true because the rational approximation √71 (8.4) is greater than the rational approximation √61 (8).
3) 81−−√ > 9
This is true because, as we mentioned earlier, the square root of 81 is exactly 9, and 9 is not greater than itself.
4) 71−−√ < 61−−√
This is false because, as we determined earlier, √71 is approximately 8.4, which is greater than √61 (8).