Using a number line, what whole number and rational number to the nearest half is √97

Question

between?

Answer 1

To find the whole number and rational number to the nearest half that $\sqrt{97}$ is between, we first need to calculate the approximate value of $\sqrt{97}$.

Calculating the square root:

$\sqrt{97}\approx 9.849$

Now we can see which whole numbers $\sqrt{97}$ falls between. The perfect squares closest to 97 are $81$ (which is $9^2$) and $100$ (which is ${10}^2$).

This means:

$$9<\sqrt{97}<10$$

Next, we find the rational number to the nearest half. The nearest halves around $9.849$ are $9.5$ and $10.0$. Since $9.849$ is closer to $10$ than to $9.5$, we round it to $9.5$.

Thus, we conclude:

• The whole number $\sqrt{97}$ is between is $9$ and $10$.
• The rational number to the nearest half that $\sqrt{97}$ is closest to is $10$.

So in summary:

$\sqrt{97}$ is between the whole numbers $9$ and $10$, and the nearest half is $10$.