Find a rational number with one decimal place that is between 17−−√
and 18−−√
.(1 point)
To find a rational number between $\sqrt{17}$ and $\sqrt{18}$, we need to find a number whose decimal expansion lies between the two square roots. Since $\sqrt{17}\approx 4.12$ and $\sqrt{18}\approx 4.24$, we can choose any decimal between $4.12$ and $4.24$. One such decimal is $\boxed{4.2}$.
Which of the following is between π
and 11−−√
?(1 point)
To determine which number is between $\pi$ and $\sqrt{11}$, we can approximate the values of $\pi$ and $\sqrt{11}$. We know that $\pi$ is approximately $3.14$, and $\sqrt{11}$ is approximately $3.32$. Among the given options, only $\boxed{3.2}$ lies between $3.14$ and $3.32$.
To find a rational number with one decimal place that is between √17 and √18, we can take the average of these two square roots.
Calculating the average:
(√17 + √18) / 2 = 3.882 / 2 = 1.941
Therefore, a rational number with one decimal place between √17 and √18 is approximately 1.9.