Question
Which of these is a rational number that comes between square root of 7 and square root of 8 In fraction form
Answers
Answered by
GPT-4o mini
To find a rational number that comes between \(\sqrt{7}\) and \(\sqrt{8}\), we first need to estimate the values of these square roots.
- \(\sqrt{7} \approx 2.64575\)
- \(\sqrt{8} = 2\sqrt{2} \approx 2.82843\)
We are looking for a rational number (a fraction) between these two values.
A simple rational number that lies between approximately 2.64575 and 2.82843 is \(\frac{17}{6}\).
Calculating \(\frac{17}{6}\):
\[
\frac{17}{6} \approx 2.83333
\]
Thus, \(\frac{17}{6}\) is indeed between \(\sqrt{7}\) and \(\sqrt{8}\).
Another option could be \(\frac{8}{3}\):
\[
\frac{8}{3} \approx 2.66667
\]
So, both \(\frac{17}{6}\) and \(\frac{8}{3}\) are examples of rational numbers between \(\sqrt{7}\) and \(\sqrt{8}\).
- \(\sqrt{7} \approx 2.64575\)
- \(\sqrt{8} = 2\sqrt{2} \approx 2.82843\)
We are looking for a rational number (a fraction) between these two values.
A simple rational number that lies between approximately 2.64575 and 2.82843 is \(\frac{17}{6}\).
Calculating \(\frac{17}{6}\):
\[
\frac{17}{6} \approx 2.83333
\]
Thus, \(\frac{17}{6}\) is indeed between \(\sqrt{7}\) and \(\sqrt{8}\).
Another option could be \(\frac{8}{3}\):
\[
\frac{8}{3} \approx 2.66667
\]
So, both \(\frac{17}{6}\) and \(\frac{8}{3}\) are examples of rational numbers between \(\sqrt{7}\) and \(\sqrt{8}\).