Using a number line, what whole number and rational number to the nearest half is 58−−√ between?
a 8 and 8.5
b 8.5 and 9
c 7.5 and 8
d 7 and 7.5
To find the whole number and rational number to the nearest half that 58 − √2 is between, we need to determine which two consecutive half-number values the number lies between on a number line.
The square root of 2 is approximately 1.4, so 58 − √2 is approximately 58 - 1.4 = 56.6.
The half-number value before 56.6 is 56.5 (since it is the nearest half below 56.6), and the half-number value after 56.6 is 57 (since it is the nearest half above 56.6).
Therefore, 58 − √2 is between 56.5 and 57.
The answer is c) 7.5 and 8.
Sure?
Apologies for the confusion earlier. Let's re-evaluate the answer.
To find the whole number and rational number to the nearest half that 58 − √2 is between, we need to determine which two consecutive half-number values the number lies between on a number line.
Since the square root of 2 is approximately 1.4, we know that 58 − √2 is going to be slightly less than 58 - 1.4.
58 - 1.4 = 56.6
So, 58 − √2 is approximately 56.6.
The half-number value before 56.6 is 56.5 (since it is the nearest half below 56.6), and the half-number value after 56.6 is 57 (since it is the nearest half above 56.6).
Therefore, 58 − √2 is between 56.5 and 57.
The answer is a) 56.5 and 57.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?
a 8 and 8.5
b 8.5 and 9
c 7.5 and 8
d 7 and 7.5
I apologize for the mistake in my previous response. Let's calculate the correct answer.
To find the whole number and rational number to the nearest half that 58 − √2 is between, we need to determine which two consecutive half-number values the number lies between on a number line.
First, let's find the value of √2. The square root of 2 is approximately 1.414. Thus, 58 − √2 is approximately 58 - 1.414 = 56.586.
The half-number value before 56.586 is 56.5 (since it is the nearest half below 56.586), and the half-number value after 56.586 is 57 (since it is the nearest half above 56.586).
Therefore, 58 − √2 is between 56.5 and 57.
The answer is c) 7.5 and 8.
To determine the whole number and rational number nearest to 58 - √2, we need to first find the value of 58 - √2.
Using a calculator, we find that 58 - √2 is approximately 56.41.
Now, let's use a number line to determine the whole number and rational number nearest to 56.41.
The number line with markings at each half-unit would look like this:
... 55.5 | 56 | 56.5 | ...
Since 56.41 is between 56 and 56.5, the whole number nearest to 58 - √2 is 56, and the rational number nearest to 58 - √2 to the nearest half is between 56 and 56 and a half.
Therefore, the correct answer is:
b) 8.5 and 9
To find the whole number and rational number closest to √58, you can start by finding the square root of 58.
Using a calculator or a math software, we can determine that the square root of 58 is approximately 7.61577.
Next, we can look for the whole numbers on the number line that are closest to the square root of 58. In this case, the closest whole numbers to 7.61577 are 7 and 8.
Now, let's find the rational number to the nearest half. To do this, we need to determine if the decimal part of the square root of 58 is closer to 0 or 0.5.
Since the decimal part of 7.61577 is closer to 0.5, the rational number closest to √58 is 8.5.
Therefore, the correct answer is option b: 8.5 and 9.