To compare $\sqrt{21}$ and $\sqrt{17}$ using rational approximations, we can find whole numbers that are close to each square root.
We know that $4^2 = 16$ and $5^2 = 25$. Since $\sqrt{17}$ is between 16 and 25, we can approximate it as $\sqrt{17} \approx 4.1$.
Similarly, we find that $5^2 = 25$ and $6^2 = 36$. Since $\sqrt{21}$ is between 25 and 36, we can approximate it as $\sqrt{21} \approx 5.8$.
Comparing the approximations, we have $4.1 < 5.8$.
Therefore, $\sqrt{21} < \sqrt{17}$.
The inequality statement is $\boxed{\sqrt{21} < \sqrt{17}}$.
Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =.
3 answers
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Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =.
Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =.
Apologies for the confusion. Let's use rational approximations to compare $\sqrt{21}$ and $\sqrt{17}$.
We can start by finding whole numbers that are close to each square root. We know that $4^2 = 16$ and $5^2 = 25$. Therefore, $\sqrt{17}$ is approximately between 4 and 5.
Now, let's find a rational approximation for $\sqrt{21}$. We know that $4^2 = 16$ and $5^2 = 25$, but $\sqrt{21}$ is closer to $\sqrt{25}$ than $\sqrt{16}$. Thus, $\sqrt{21}$ is approximately between 4 and 5 as well.
Since both square roots have the same rational approximation range of 4 to 5, we can conclude that $\sqrt{21}$ and $\sqrt{17}$ are approximately equal, or in inequality notation, $\sqrt{21} \approx \sqrt{17}$. Thus, the inequality statement is $\boxed{\sqrt{21} \approx \sqrt{17}}$.
We can start by finding whole numbers that are close to each square root. We know that $4^2 = 16$ and $5^2 = 25$. Therefore, $\sqrt{17}$ is approximately between 4 and 5.
Now, let's find a rational approximation for $\sqrt{21}$. We know that $4^2 = 16$ and $5^2 = 25$, but $\sqrt{21}$ is closer to $\sqrt{25}$ than $\sqrt{16}$. Thus, $\sqrt{21}$ is approximately between 4 and 5 as well.
Since both square roots have the same rational approximation range of 4 to 5, we can conclude that $\sqrt{21}$ and $\sqrt{17}$ are approximately equal, or in inequality notation, $\sqrt{21} \approx \sqrt{17}$. Thus, the inequality statement is $\boxed{\sqrt{21} \approx \sqrt{17}}$.