Using a number line, what whole number and rational number to the nearest half is √58 between
1. Between 8.5 and 9
2. Between 7.5 and 8
3. Between 8 and 8.5
4. Between 7 and 7.5
To solve this problem, we can start by finding the whole numbers that √58 is between on the number line.
1. Between 8.5 and 9:
The whole number 9 is the higher bound, and we can square this number to find its square root: √(9^2) = √81 = 9.
Since √58 is less than 9, it must be between 8 and 8.5.
2. Between 7.5 and 8:
The whole number 8 is the higher bound, and we can square this number to find its square root: √(8^2) = √64 = 8.
Since √58 is less than 8, it must be between 7.5 and 8.
3. Between 8 and 8.5:
The whole number 8.5 is the higher bound, and we can square this number to find its square root: √(8.5^2) is approximately 9.192.
Since √58 is less than 9.192 and greater than 8, it is between 8 and 8.5.
4. Between 7 and 7.5:
The whole number 7.5 is the higher bound, and we can square this number to find its square root: √(7.5^2) is approximately 8.660.
Since √58 is less than 8.660 and greater than 8, it is between 7 and 7.5.
Therefore, the answer is:
1. Between 8 and 8.5.
2. Between 7.5 and 8.
3. Between 8 and 8.5.
4. Between 7 and 7.5.
may i have one answer which one is right??
Apologies for the confusion. Here is the correct answer:
Out of the given options, the nearest whole number and rational number to the nearest half that √58 is between are:
1. Between 8 and 8.5.
To find the whole number and rational number to the nearest half for √58, we need to determine the two consecutive numbers on a number line that √58 falls between.
1. Between 8.5 and 9:
We square both numbers to compare them to 58: (√8.5)^2 = 8.5 and (√9)^2 = 9. Since 58 falls between 8.5 and 9, we can conclude that √58 is between √8.5 and √9.
√8.5 is approximately 2.915, and √9 is exactly 3.
2. Between 7.5 and 8:
Similarly, we square both numbers: (√7.5)^2 = 7.5 and (√8)^2 = 8. Since 58 falls between 7.5 and 8, we can say √58 is between √7.5 and √8.
√7.5 is approximately 2.74, and √8 is exactly 2.8284.
3. Between 8 and 8.5:
If we square these numbers, we get (√8)^2 = 8 and (√8.5)^2 = 8.5. Since 58 falls between 8 and 8.5, we can determine that √58 is between √8 and √8.5.
√8 is exactly 2.8284, and √8.5 is approximately 2.915.
4. Between 7 and 7.5:
For these numbers, (√7)^2 = 7 and (√7.5)^2 = 7.5. Since 58 falls between 7 and 7.5, we can conclude that √58 is between √7 and √7.5.
√7 is approximately 2.6458, and √7.5 is approximately 2.74.
In summary, the results are:
1. Between 8.5 and 9: √58 is between 2.915 and 3.
2. Between 7.5 and 8: √58 is between 2.74 and 2.8284.
3. Between 8 and 8.5: √58 is between 2.8284 and 2.915.
4. Between 7 and 7.5: √58 is between 2.6458 and 2.74.
To determine the whole number and rational number closest to √58, we need to calculate the value of √58 first.
1. Between 8.5 and 9:
- To find the value of √58, we note that √49 = 7 and √64 = 8.
- Since 58 is between 49 and 64, √58 will be between 7 and 8.
- The midpoint between 8.5 and 9 is 8.75.
- √58 is closer to 8.75 than to 9.
2. Between 7.5 and 8:
- Again, we recall that √49 = 7 and √64 = 8.
- As 58 lies between 49 and 64, √58 will be between 7 and 8.
- The midpoint between 7.5 and 8 is 7.75.
- √58 is closer to 7.75 than to 7.5.
3. Between 8 and 8.5:
- We already know that √58 is between 7 and 8.
- The midpoint between 8 and 8.5 is 8.25.
- √58 is closer to 8.25 than to 8.
4. Between 7 and 7.5:
- As we established earlier, √58 is between 7 and 8.
- The midpoint between 7 and 7.5 is 7.25.
- √58 is closer to 7.25 than to 7.
Based on the above analysis, we can conclude:
- √58 is closer to 8.75 than to 9 and hence, closest whole number is 9.
- √58 is closer to 7.75 than to 7.5 and hence, closest rational number to the nearest half is 7.5.
Therefore, the whole number and rational number closest to √58 are 9 and 7.5, respectively.