Approximate Values of Irrational Numbers Quick Check
Math 8 Q1 (Pre-Algebra) / The Number System
Using a number line, what is the approximate value of 19−−√?(1 point)
Responses
4.13
4.38
4.5
4.25
these are wrong
The approximate value of √19 can be found by finding the perfect squares that are closest to 19 on either side. The perfect square that is less than 19 is 16 (4^2) and the perfect square that is greater than 19 is 25 (5^2). Since √16 is 4 and √25 is 5, we can estimate that √19 is approximately between 4 and 5. Looking at the answer choices, the closest value to this estimate is 4.38. Therefore, the approximate value of √19 is 4.38.
Approximate Values of Irrational Numbers Quick Check
Math 8 Q1 (Pre-Algebra) / The Number System
Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
Responses
between 11 and 11.5
between 11 and 11.5
between 9.5 and 10
between 9.5 and 10
between 10 and 10.5
between 10 and 10.5
between 10.5 and 11
To find which whole number and rational number to the nearest half √105 is between, we can use a number line. The perfect squares that are closest to 105 on either side are 100 (10^2) and 121 (11^2). Since √100 is 10 and √121 is 11, we know that √105 is between 10 and 11.
To find which rational number to the nearest half, we can divide the interval between 10 and 11 into halves.
10 + 0.5 = 10.5
So, √105 is between the whole number 10 and the rational number 10.5.
Therefore, the correct answer is "between 10 and 10.5."
Approximate Values of Irrational Numbers Quick Check
Math 8 Q1 (Pre-Algebra) / The Number System
Using rational approximations, what statement is true?(1 point)
Responses
49−−√<7
start root 49 end root less than 7
48−−√<36−−√
start root 48 end root less than start root 36 end root
49−−√>7
start root 49 end root greater than 7
48−−√>36−−√
To find the rational approximations for √49, we can try different perfect squares that are closest to 49. The perfect square that is less than 49 is 36 (6^2) and the perfect square that is greater than 49 is 64 (8^2). Since √36 is 6 and √64 is 8, we can estimate that √49 is between 6 and 8.
The first statement, "49−−√<7", claims that the square root of 49 is less than 7. However, since we estimated that √49 is between 6 and 8, this statement is not true.
The second statement, "48−−√<36−−√", is comparing the square roots of 48 and 36. This statement is not relevant to our approximation task, as it does not provide comparisons between √49 and any other numbers. Therefore, this statement is not true.
The third statement, "49−−√>7", claims that the square root of 49 is greater than 7. Based on our estimation, √49 is between 6 and 8, so this statement is not true.
The fourth statement, "48−−√>36−−√", is also comparing the square roots of 48 and 36. Like the second statement, this statement is not relevant to our task and does not provide information about the square root of 49. Therefore, this statement is not true.
In conclusion, none of the provided statements are true.
which statement is true
Approximate Values of Irrational Numbers Quick Check
Math 8 Q1 (Pre-Algebra) / The Number System
Using rational approximations, what statement is true?(1 point)
Responses
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
71−−√>61−−√
start root 71 end root greater than start root 61 end root
81−−√<9
start root 81 end root less than 9
81−−√>9
To find the rational approximations for √71 and √61, we can try different perfect squares that are closest to these numbers. The perfect square that is less than 71 is 64 (8^2) and the perfect square that is greater than 71 is 81 (9^2). Since √64 is 8 and √81 is 9, we can estimate that √71 is between 8 and 9.
Similarly, the perfect square that is less than 61 is 49 (7^2) and the perfect square that is greater than 61 is 64 (8^2). Since √49 is 7 and √64 is 8, we can estimate that √61 is between 7 and 8.
Now let's evaluate the given statements based on these estimations:
1. "71−−√<61−−√": Since √71 is estimated to be between 8 and 9, while √61 is estimated to be between 7 and 8, it is true that √71 is greater than √61. Therefore, this statement is not true.
2. "71−−√>61−−√": As mentioned above, √71 is estimated to be between 8 and 9, while √61 is estimated to be between 7 and 8. Therefore, it is true that √71 is greater than √61. Thus, this statement is true.
3. "81−−√<9": Since √81 is equal to 9, it is not less than 9. Therefore, this statement is not true.
4. "81−−√>9": Since √81 is equal to 9, it is not greater than 9. Therefore, this statement is not true.
In conclusion, the true statement is "71−−√>61−−√".
Approximate Values of Irrational Numbers Quick Check
Math 8 Q1 (Pre-Algebra) / The Number System
Using rational approximations, what statement is true?(1 point)
Responses
16−−√>4
start root 16 end root greater than 4
12 −−−√ >wπ
start root 12 end root greater than pi
12 −−−√<π
start root 12 end root less than pi
16 −−−√<4