What whole number and rational number to the nearest half is √20 between?
To find the whole number and rational number to the nearest half that √20 is between, we can first find the approximate value of √20.
√20 is approximately 4.47.
The nearest half numbers to 4.47 are 4.5 and 4. Therefore, since √20 is between 4 and 4.5, √20 is between the whole number 4 and the rational number 4.5 to the nearest half.
What is a rational number with a denominator of 4 that is between √5 and √6?
To find a rational number with a denominator of 4 that is between √5 and √6, we can first convert √5 and √6 into decimal approximations.
√5 is approximately 2.236.
√6 is approximately 2.449.
Next, we can find rational numbers with a denominator of 4 that are between these decimal approximations. We can start with the lower bound:
Lower bound:
√5 is approximately 2.236.
2.236 can be written as 2 + (1/4).
Upper bound:
√6 is approximately 2.449.
2.449 can be written as 2 + (1/2) + (3/4).
Therefore, we can conclude that a rational number with a denominator of 4 that is between √5 and √6 is between 2 + (1/4) and 2 + (1/2) + (3/4).
so what's the answer
The rational number with a denominator of 4 that is between √5 and √6 is between 2 + (1/4) and 2 + (1/2) + (3/4).
To find the whole number that is closest to √20, we can take the floor of √20. The floor function rounds down to the nearest whole number.
Floor(√20) = Floor(4.4721) = 4
Next, to find a rational number to the nearest half, we need to determine if √20 is closer to 4 or 5. To do this, we can calculate the difference between √20 and 4.5 and compare it with the difference between √20 and 3.5.
|√20 - 4.5| = |4.4721 - 4.5| = 0.0279
|√20 - 3.5| = |4.4721 - 3.5| = 0.9721
Since 0.0279 is smaller than 0.9721, √20 is closer to 4.5 than 3.5.
Therefore, the number that is both a whole number and a rational number to the nearest half that √20 is in between is 4.5.
To find the whole number and rational number to the nearest half that √20 is between, we need to determine the two consecutive numbers whose squares are closest to 20.
1. Start by finding the square of whole numbers near the square root of 20. The square of 4 is 16, and the square of 5 is 25. Since 20 is between these two values, the whole number part is 4.
2. To find the nearest half, we take the square root of 20 and subtract the whole number part (4). We are left with √20 - 4.
3. Next, divide the result from step 2 by 1. This will give us a decimal value.
(√20 - 4) ÷ 1 = √20 - 4
4. To get the decimal value to the nearest half, we need to round the result from step 3 to the nearest 0.5. In this case, the result is approximately 0.472.
5. To find the whole number and rational number to the nearest half, we add this rounded decimal value to the whole number part (4).
4 + 0.5 = 4.5
Therefore, to the nearest half, √20 is between the whole number 4 and the rational number 4.5.