Using a number line, what whole number and rational number to the nearest half is square root of 40 between?

Question

Square root of 40 is between ____and___.

Answer 1

To find the whole number and the rational number to the nearest half that \(\sqrt{40}\) is between, let's first calculate the approximate value of \(\sqrt{40}\).

\[ \sqrt{40} \approx 6.32 \]

Now let's determine the whole numbers it lies between. Since \(6.32\) is greater than \(6\) and less than \(7\), we can identify that:

\(\sqrt{40}\) is between 6 and 7.

Next, let's round \(\sqrt{40}\) to the nearest half. The nearest halves surrounding \(6.32\) are \(6.0\) and \(6.5\). Since \(6.32\) is closer to \(6.5\) than \(6.0\), we can conclude that:

\(\sqrt{40}\) rounded to the nearest half is approximately 6.5.

Putting this together, we can conclude:

\(\sqrt{40}\) is between 6 and 7, and rounded to the nearest half, it is approximately 6.5.

Answer 2

Using a number line, what whole number and rational number to the nearest half is square root of 58 between?
A)between 8 and 8.5
B)between 7 and 7.5
C)between 7 and 7.5
D) between 8.5 and 9

Answer 3

To determine the whole number and the rational number to the nearest half that \(\sqrt{58}\) is between, we first need to calculate the approximate value of \(\sqrt{58}\).

Calculating the square root:

\[ \sqrt{58} \approx 7.62 \]

Now let's see between which whole numbers \(\sqrt{58}\) lies. Since \(7.62\) is greater than \(7\) but less than \(8\), we can confirm that:

\(\sqrt{58}\) is between 7 and 8.

Next, let's round \(\sqrt{58}\) to the nearest half. The nearest halves surrounding \(7.62\) are \(7.5\) and \(8.0\). Since \(7.62\) is closer to \(7.5\) than to \(8.0\), we see that it approximates to:

\(\sqrt{58}\) is approximately 7.5 when rounded to the nearest half.

Now let's match this information with the options provided:

A) between 8 and 8.5
B) between 7 and 7.5
C) between 7 and 7.5
D) between 8.5 and 9

The values of \(\sqrt{58} \approx 7.62\) show that it is closer to \(8\) than to \(7.5\), but because the options are choosing ranges, it should fit into option C (between 7 and 7.5) as \(\sqrt{58}\) is approximately \(7.62\) which is indeed more accurately rounded than being above or around \(7.5\).

Final answers:

Whole number: between 7 and 8
Rational number to the nearest half: approximately 7.5
Thus, the main option to select based on proximity should be C) between 7 and 7.5.

Answer 4

Using a number line, what whole number and rational number to the nearest half is square root of 58 between?
A)between 8 and 8.5
B)between 7 and 7.5
C)between 7.5 and 8
D) between 8.5 and 9

Answer 5

To determine the whole number and the rational number to the nearest half that \(\sqrt{58}\) is between, we first estimate the value of \(\sqrt{58}\).

Calculating the square root:

\[ \sqrt{58} \approx 7.62 \]

Now we identify the whole numbers it lies between. Since \(7.62\) is greater than \(7\) but less than \(8\), we conclude that:

\(\sqrt{58}\) is between 7 and 8.

Next, we round \(\sqrt{58}\) to the nearest half. The nearest halves surrounding \(7.62\) are \(7.5\) and \(8.0\). Since \(7.62\) is closer to \(7.5\) than to \(8.0\), we approximate that:

\(\sqrt{58}\) rounds to 7.5.

Now let’s evaluate the options based on our calculations:

A) between 8 and 8.5
B) between 7 and 7.5
C) between 7.5 and 8
D) between 8.5 and 9

Since \(7.62\) is greater than \(7.5\) but less than \(8\), it fits into option C (between 7.5 and 8).

Final Answer:

Whole number: Between 7 and 8
Rational number to the nearest half: Rounds to \(7.5\)
Thus, the correct option is C) between 7.5 and 8.