Show an example of an irrational number between 9 and 11.(1 point)
Responses
20−−√
start root 20 end root
99−−√
start root 99 end root
10−−√
start root 10 end root
100−−−√
start root 100 end root
What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses
6
6
25
25
26
26
13
13
Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
165
Start Fraction 16 over 5 end fraction
103
Start Fraction 10 over 3 end fraction
3.4
3.4
Start Fraction 103 over 32 end fraction
Which irrational number is between 14−−√ and 18−−√?(1 point)
Responses
15−−√
start root 15 end root
13−−√
start root 13 end root
10−−√
start root 10 end root
19−−√
start root 17 end root
How many irrational numbers are there between 11−−√ and 17−−√?(1 point)
Responses
twenty-eight numbers
twenty-eight numbers
six numbers
six numbers
an infinite number
an infinite number
four numbers
an infinite number
To find an example of an irrational number between 9 and 11, you can consider the square root (√) of a nonperfect square number. A nonperfect square number is a number that cannot be expressed as an integer multiplied by itself.
Let's calculate the square root of some numbers within the given range and determine if they are irrational:
1. √20 ≈ 4.47
The square root of 20 is approximately 4.47, which is an irrational number. This falls between 9 and 11.
2. √99 ≈ 9.95
The square root of 99 is approximately 9.95, which is also an irrational number. It falls within the given range.
3. √10 ≈ 3.16
The square root of 10 is approximately 3.16, which is another irrational number that falls between 9 and 11.
4. √100 = 10
The square root of 100 is equal to 10. Since it is a perfect square and not between 9 and 11, it is not an example of an irrational number within the given range.
Therefore, the correct answer is √20, as it is an irrational number that falls between 9 and 11.