what whole number and rational number to the nearest half is 97−−√ between?
To find the whole number and rational number to the nearest half that is between $\sqrt{97}$, we can compare $\sqrt{97}$ to the squares of the numbers near it to determine which whole number $\sqrt{97}$ is closest to.
We can make a table of some perfect squares: $$ \begin{array}{c|c} x & x^2 \\ \hline 9 & 81 \\ 10 & 100 \\ 11 & 121 \\ \end{array} $$We see that $9^2=81<97<100=10^2$. Therefore, we know that $\sqrt{97}$ is between $9$ and $10$.
To find the rational number to the nearest half that is between $\sqrt{97}$, we need to compare $\sqrt{97}$ to the squares of the numbers halfway between $9$ and $10$.
We can make a similar table of some perfect squares: $$ \begin{array}{c|c} x & x^2 \\ \hline 9\frac{1}{2} & 90\frac{1}{4} \\ \\ 9\frac{3}{4} & 95\frac{7}{16} \\ \\ 9\frac{7}{8} & 96\frac{49}{64} \\ \\ 9\frac{15}{16} & 97\frac{225}{256} \\ \\ 10 & 100 \\ \end{array} $$We see that $\displaystyle 9\frac{7}{8} = \frac{79}{8}$ is largest square less than $97$. Therefore, $\sqrt{97}$ is between $9\frac{7}{8}$ and $10$, which simplified is $\boxed{\frac{79}{8}}$.
To find the whole number and rational number to the nearest half that is between √97, we can start by finding the integer value of √97.
Calculating √97 gives us approximately 9.8488.
To find the whole number and rational number to the nearest half, we need to look at the decimal part after the whole number. In this case, the decimal part is 0.8488.
Since 0.8488 is less than 0.5, we round down to the nearest half, which is 9.5.
Therefore, the whole number and rational number to the nearest half that is between √97 is 9.5.