Show an example of an irrational number between 9 and 11.(1 point)
Responses
99−−√
start root 99 end root
100−−−√
start root 100 end root
20−−√
start root 20 end root
10−−√
start root 10 end root
What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses
6
6
13
13
25
25
26
26
Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
16/5
Start Fraction 16 over 5 end fraction
3.1
3.1
3.4
3.4
10/3
10/3
Numbers Between Rational Numbers Quick Check
4 of 54 of 5 Items
Question
Which irrational number is between 14−−√ and 18−−√?(1 point)
Responses
10−−√
start root 10 end root
19−−√
start root 19 end root
15−−√
start root 15 end root
13−−√
15−−√ (start root 15 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, we need to look for a number that cannot be expressed as a fraction and its square root is not exactly equal to any whole number or fraction.
Let's consider the square root of 10 (√10). To determine if √10 is an irrational number, we can use an approximation method, such as a calculator or estimation technique.
Taking the square root of 10 on a calculator gives us approximately 3.16227766. This number continues indefinitely without repeating or terminating, indicating that it is irrational.
Therefore, one example of an irrational number between 9 and 11 is √10, with an approximate value of 3.16227766.