Using a number line, what whole number and rational number to the nearest half is 40√ between?
To determine the whole number and rational number to the nearest half that 40√ falls between, we need to determine the value of 40√ and find the whole number and rational number that is closest to it.
First, let's find the value of 40√:
40√ = 40 * √(1)
= 40 * (√(2^2) * √(10))
= 40 * (2 * √(10))
= 80√(10)
Now, let's find the whole number and rational number closest to 80√(10) to the nearest half using a number line:
- Using a calculator, we find that √(10) is approximately 3.162.
- Thus, 80√(10) is approximately 80 * 3.162 = 252.96.
On the number line, the whole number and rational number closest to 252.96 to the nearest half are:
252.5 and 253.
Therefore, the whole number and rational number to the nearest half that 40√ falls between are 252.5 and 253.
Using a number line, what whole number and rational number to the nearest half is √40 between?
To find the whole number and the rational number to the nearest half that 40√ is between on a number line, we first need to determine the approximate value of 40√.
The square root (√) of a number can be estimated by using a calculator or by finding the square root of the closest perfect square. Since 40 is between 36 (6²) and 49 (7²), the square root of 40 would be between 6 and 7.
To find the approximate value of 40√, we can take the square root of 40 by calculating √40 as follows:
√40 ≈ √36 + (√40 - √36)
√40 ≈ 6 + (√40 - 6)
Now, let's calculate the value of √40 - 6:
√40 - 6 = √(4 * 10) - 6
√40 - 6 = 2√10 - 6
Since √10 is between 3 and 4, we can estimate its value as 3.5:
√10 ≈ 3.5
Now, substituting this value back into √40 - 6:
√40 - 6 ≈ (2 * 3.5) - 6
√40 - 6 ≈ 7 - 6
√40 - 6 ≈ 1
Therefore, the approximate value of 40√ is 6 + 1 = 7.
To find the whole number and rational number to the nearest half that 40√ is between on the number line, we can consider the intervals around 7. The number line can be divided into intervals of size 0.5, with 7 being the middle of one such interval.
Thus, the whole number and rational number to the nearest half that 40√ is between are:
Whole Number: 7
Rational Number: 7.5
To find the whole number and rational number closest to 40√ on a number line, we need to first understand what the term "between" means in this context. It means that we are looking for numbers that sandwich 40√ with a smaller number on one side and a larger number on the other side.
Let's start by approximating the value of 40√. Because the square root of any number is always positive, we only need to consider positive numbers. We can take a reasonable guess by finding the square root of the closest perfect square to 40, which is 36. The square root of 36 is 6.
So, we can estimate that the value of 40√ is around 6 times the square root of 10, which is roughly 6 x 3.16 = 18.96.
Now, let's find the whole number and rational number to the nearest half that is closest to 18.96.
The whole number closest to 18.96 is 19.
To find the rational number to the nearest half, we consider the half-point values on either side of 18.96, which are 18.5 and 19.5.
Therefore, to the nearest half, the whole number and rational number that sandwich 40√ are 19 and 19.5, respectively.
So, the answer is:
Whole Number: 19
Rational Number to the nearest half: 19.5