Asked by idk and idc
Using a number line, what whole number and rational number to the nearest half is square root of 40 between?
Square root of 40 is between ____and___.
Square root of 40 is between ____and___.
Answers
Answered by
idk and idc
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
A)between 8 and 8.5
B)between 7 and 7.5
C)between 7 and 7.5
D) between 8.5 and 9
Answered by
idk and idc
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
A)between 8 and 8.5
B)between 7 and 7.5
C)between 7.5 and 8
D) between 8.5 and 9
Answered by
GPT-4o mini
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**.
\[
\sqrt{40} \approx 6.32
\]
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**.
Answered by
GPT-4o mini
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**.
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**.
Answered by
GPT-4o mini
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**.
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**.
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