Question
Which of these is a rational number that comes between square root of 7 and square root of 8
Answers
Answered by
GPT-4o mini
To find a rational number that lies between \(\sqrt{7}\) and \(\sqrt{8}\), we can start by calculating the approximate values of these square roots:
\[
\sqrt{7} \approx 2.64575
\]
\[
\sqrt{8} = 2\sqrt{2} \approx 2.82843
\]
Now, to find a rational number between these two values, we can observe that various simple fractions fall within this range.
For example, \(2.7\) is a rational number that lies between \(\sqrt{7}\) and \(\sqrt{8}\):
\[
\sqrt{7} \approx 2.64575 < 2.7 < 2.82843 \approx \sqrt{8}
\]
Thus, one rational number that lies between \(\sqrt{7}\) and \(\sqrt{8}\) is:
\[
\frac{27}{10} = 2.7
\]
There are many other rational numbers that would also fit in this interval, such as \(2.6\), \(2.75\), or \(2.8\), but \(2.7\) is a straightforward choice.
\[
\sqrt{7} \approx 2.64575
\]
\[
\sqrt{8} = 2\sqrt{2} \approx 2.82843
\]
Now, to find a rational number between these two values, we can observe that various simple fractions fall within this range.
For example, \(2.7\) is a rational number that lies between \(\sqrt{7}\) and \(\sqrt{8}\):
\[
\sqrt{7} \approx 2.64575 < 2.7 < 2.82843 \approx \sqrt{8}
\]
Thus, one rational number that lies between \(\sqrt{7}\) and \(\sqrt{8}\) is:
\[
\frac{27}{10} = 2.7
\]
There are many other rational numbers that would also fit in this interval, such as \(2.6\), \(2.75\), or \(2.8\), but \(2.7\) is a straightforward choice.