Question

Using a number line, what whole number and rational number to the nearest half is 97−−√ between?(1 point)

Answer 1

using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =.(1 point)

Answer 2

Using rational approximations, what is an inequality statement comparing π and 8–√? Enter <, >, or =.(1 point)

Answer 3

On a number line, we can find the whole number and rational number to the nearest half that is closest to $\sqrt{97}$.

First, we find the two perfect squares on either side of 97: $9^2=81$ and $10^2=100$.

Since $9^2<97<10^2$, we know that $\sqrt{97}$ is between 9 and 10.

Next, we find the midpoint between 9 and 10, which is $\frac{9+10}{2}=\frac{19}{2}=\boxed{9.5}$. Therefore, the whole number and rational number to the nearest half that is closest to $\sqrt{97}$ is 9.5.

Answer 4

To compare $\sqrt{21}$ and $\sqrt{17}$ using rational approximations, we can find the integers closest to each square root.

For $\sqrt{21}$:

$4^2 = 16$ and $5^2 = 25$

Since $16 < 21 < 25$, we know that $\sqrt{21}$ is between 4 and 5.

For $\sqrt{17}$:

$4^2 = 16$ and $5^2 = 25$

Since $16 < 17 < 25$, we know that $\sqrt{17}$ is also between 4 and 5.

Therefore, $\sqrt{21}$ and $\sqrt{17}$ are both between 4 and 5.

Inequality statement: $\sqrt{21}$ = $\sqrt{17}$.

$\boxed{=}$

Answer 5

To compare $\pi$ and $\sqrt{8}$ using rational approximations, we can use the fact that $\pi$ is an irrational number approximately equal to 3.14.

For $\sqrt{8}$:

$2^2 = 4$ and $3^2 = 9$

Since $4 < 8 < 9$, we know that $\sqrt{8}$ is between 2 and 3.

Therefore, $\pi$ is approximately 3.14, which is larger than $\sqrt{8}$.

Inequality statement: $\pi > \sqrt{8}$.

$\boxed{>}$