Which of the following is an irrational number between 5 and 7: √6, √12, √27, or √36?
An irrational number is a number that cannot be expressed as a simple fraction or as a decimal that terminates or repeats.
√6 ≈ 2.449
√12 ≈ 3.464
√27 ≈ 5.196
√36 = 6
Among the given options, √6 and √12 are irrational numbers. However, only √6 is between 5 and 7.
Show an example of an irrational number between 9 and 11.
√100
√20
√10
√99
Among the given options, √10 is an irrational number between 9 and 11.
√10 ≈ 3.162
Therefore, √10 is an example of an irrational number between 9 and 11.
What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
13
6
26
25
The least integer whose square root is an irrational number between 5 and 7 is 26.
√26 ≈ 5.099
Show an example of a rational number that is between √10 and √11.
3.4
10/3 (10 over 3 fraction)
16/5 (16 over 5 fraction)
3.1
Among the given options, 10/3 is a rational number that is between √10 and √11.
√10 ≈ 3.162
√11 ≈ 3.317
10/3 ≈ 3.333
Therefore, 10/3 is an example of a rational number between √10 and √11.
Which irrational number is between 14−−√ and 18−−√?
√10
√19
√15
√13
To determine which irrational number is between $\sqrt{14}$ and $\sqrt{18}$, we can approximate the square roots:
$\sqrt{14} \approx 3.742$
$\sqrt{18} \approx 4.243$
Among the given options, $\sqrt{15}$ is the only irrational number that falls between these approximations:
$\sqrt{15} \approx 3.873$
Therefore, $\sqrt{15}$ is the irrational number between $\sqrt{14}$ and $\sqrt{18}$.
How many irrational numbers are there between √11 and √17?
four numbers
an infinite number
six numbers
twenty-eight numbers
To determine the number of irrational numbers between $\sqrt{11}$ and $\sqrt{17}$, we need to consider that irrational numbers are infinite in between any two distinct numbers.
$\sqrt{11} \approx 3.317$
$\sqrt{17} \approx 4.123$
Since we have an infinite number of rational numbers between these approximations, the correct answer is that there are an infinite number of irrational numbers between $\sqrt{11}$ and $\sqrt{17}$.