The Number System Unit Test
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Question
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between
and
.
To solve this problem, we need to consider that the square root of 40 is approximately 6.32. Since we are looking for the rational number to the nearest half, we need to determine the whole numbers and the rational numbers that are closest to 6.32.
On the number line, we can see that the integer 6 lies to the left of 6.32, and the integer 7 lies to the right.
To determine the rational number to the nearest half, we need to compare the distance from 6.32 to 6.5 (to the right) and the distance from 6.32 to 6 (to the left).
The distance from 6.32 to 6.5 is 0.18,
The distance from 6.32 to 6 is 0.32.
So, the rational number to the nearest half for 40−−√ is between 6 and 6.5.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between
and
.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?
To find the whole number and rational number to the nearest half that 40−−√ is between, we can use a number line to visualize the range.
Given that 40−−√ is between two numbers, let's call the first number "x" and the second number "y".
To begin, we can start by finding the whole number value for 40−−√. Since 40−−√ is approximately 6.32 (rounded to two decimal places), the whole number value for 40−−√ is 6.
Next, we can find the rational number to the nearest half by looking at the decimal portion of 40−−√. The decimal portion of 6.32 (40−−√) is 0.32. To convert this decimal to the nearest half, we can round it to the nearest multiple of 0.5. Since 0.32 is closer to 0.5 than 0, we will round up to 0.5.
Therefore, the rational number to the nearest half for 40−−√ is 0.5.
Putting it all together, we can say 40−−√ is between 6 and 6.5 on a number line.
To determine what whole number and rational number to the nearest half 40−−√ is between, we first need to understand what 40−−√ represents.
The symbol √ denotes the square root function. So 40−−√ means the square root of 40.
To find what whole number and rational number 40−−√ is between, we can use a number line. We will start by calculating the exact value of the square root of 40.
To calculate the square root of 40, we can use a calculator or find an approximate value by hand.
By hand, we can recognize that 6 is a square root of 36 and 7 is a square root of 49. Since the number 40 is closer to 36, we know that the square root of 40 is slightly greater than 6 but less than 7.
Next, let's use a number line to find the whole number and rational number that 40−−√ is between.
On the number line, let's plot the whole numbers 6 and 7.
5 6 7 8 9 ...
↑
Now, we can estimate the location of 40−−√ on the number line.
Since the square root of 40 is slightly greater than 6, we can place it closer to 7.
5 6 7 8 9 ...
↑
Now, to find the nearest half, we can divide the interval between 6 and 7 into halves.
5 6 6.5 7 7.5 ...
↑
From the number line, we can see that the whole number and rational number to the nearest half that 40−−√ is between are 6.5 and 7.
Therefore, 40−−√ is between 6.5 and 7.
Using a number line what whole number and rational to the nearest half is 58 squared between
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 8 and 8.5
between 8 and 8.5
between 8.5 and 9
between 8.5 and 9
between 7.5 and 8
between 7.5 and 8
between 7 and 7.5