What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
The least integer whose square root is an irrational number between 5 and 7 is 26.
Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
An example of a rational number that is between $\sqrt{10}$ and $\sqrt{11}$ is $\frac{22}{7}$. Simplifying, we have $\sqrt{10} \approx 3.162$ and $\sqrt{11} \approx 3.317$, so $\frac{22}{7} \approx 3.143$, which is between $\sqrt{10}$ and $\sqrt{11}$.
the only answers are 3.1, 10/3, 16/5, and 3.4
My apologies for the incorrect response. You are correct. Some examples of rational numbers between $\sqrt{10}$ and $\sqrt{11}$ are $\frac{31}{10}$ and $\frac{34}{10}$, which can be simplified to $3.1$ and $3.4$ respectively.
which one is the answer bot
The answer is $3.1$.
Which irrational number is between 14−−√ and 18−−√?(1 point)
An irrational number that is between $\sqrt{14}$ and $\sqrt{18}$ is $\sqrt{16}$. Simplifying, we have $\sqrt{14} \approx 3.742$ and $\sqrt{18} \approx 4.243$, so $\sqrt{16} = 4$ is between $\sqrt{14}$ and $\sqrt{18}$.
the only answers are square root 15, square root 19, square root 10, square root 13.
Apologies for the incorrect response. You are correct. The irrational number that is between $\sqrt{14}$ and $\sqrt{18}$ is $\sqrt{15}$.
How many irrational numbers are there between 11−−√ and 17−−√?(1 point)
To determine how many irrational numbers are between $\sqrt{11}$ and $\sqrt{17}$, we can count the number of perfect squares between 11 and 17.
The perfect squares between 11 and 17 are 16 (4^2) and 9 (3^2).
Therefore, there is only one perfect square between $\sqrt{11}$ and $\sqrt{17}$.
Since the irrational numbers are infinite and densely populated between any two distinct numbers, there are an infinite number of irrational numbers between $\sqrt{11}$ and $\sqrt{17}$.