Using a number line, what whole number and rational number to the nearest half is 58−−√ between?

Question

Using a number line, what whole number and rational number to the nearest half is 58−−√ between?

Answer 1

Using a number line, what whole number and rational number to the nearest half is −−√ 58 between?

Answer 2

To find the whole number and rational number to the nearest half that is between $\sqrt{58}$, we need to identify the whole numbers and rational numbers closest to $\sqrt{58}$ on a number line.

First, let's find the whole number closest to $\sqrt{58}$. We know that $\sqrt{49} = 7$ and $\sqrt{64} = 8$. Since $\sqrt{58}$ is greater than $\sqrt{49}$ but less than $\sqrt{64}$, we can conclude that the closest whole number is 7.

Next, let's find the rational number to the nearest half. We know that $\sqrt{58}$ is between $\sqrt{49}$ and $\sqrt{64}$, which correspond to 7 and 8 on the number line. We can divide the interval between 7 and 8 into halves.

The midpoint between 7 and 8 is $\frac{7+8}{2} = \frac{15}{2} = 7.5$. Since $\sqrt{58}$ is closer to 7 than to 8, the rational number to the nearest half is 7.

Therefore, the whole number and rational number to the nearest half that is between $\sqrt{58}$ are 7 and $\frac{7}{2}$, respectively.

Answer 3

To find the whole number and rational number to the nearest half for the number √58, we can start by calculating the value of √58.

Using a calculator or approximation methods, we find that √58 is approximately 7.61577

Next, let's plot this value on a number line. We'll create a number line with intervals of 0.5 and place the value of √58 on it.

... 7 7.5 8 ...

Since √58 is closer to 8 than 7, we can conclude that the whole number to the nearest half is 8.

Now, let's determine the rational number to the nearest half by considering the two closest half points on the number line, which are 7.5 and 8.

... 7 7.5 8 ...

Since √58 is closer to 8, we can take 8 as our rational number to the nearest half.

Therefore, the whole number and rational number to the nearest half for √58 are:

Whole number: 8
Rational number: 8

Answer 4

To determine the whole number and rational number to the nearest half that is closest to $\sqrt{58}$, we can compare it to the square root of the surrounding perfect squares. Since $7^2=49$ and $8^2=64$, we have $7<\sqrt{58}<8$. Writing the square root as a fraction, we get $\frac{\sqrt{58}}{1}$. To simplify this fraction, we multiply by $\frac{1}{\sqrt{58}}$: $$\frac{\sqrt{58}}{1}\cdot\frac{\sqrt{58}}{\sqrt{58}}=\frac{58}{\sqrt{58}}.$$ Rationalizing the denominator, we obtain $\frac{58}{\sqrt{58}}=\frac{58}{\sqrt{58}}\cdot\frac{\sqrt{58}}{\sqrt{58}}=\frac{58\sqrt{58}}{58}=\sqrt{58}$. Notice that $\frac{7}{\sqrt{58}}<1$ since $\sqrt{58}<7$. Similarly, $\frac{8}{\sqrt{58}}>1$ since $\sqrt{58}<8$. Thus, $\boxed{\frac{7}{2}}$ and $\boxed{\frac{8}{2}=4}$ are the whole number and rational number to the nearest half, respectively.