Which of the following rational numbers is not between the square root of 3 and the square root of 6?
A. 1.8
B. √4
C. 1.5
D. 2
Can you explain in more detail?
what rubbish.
√3 = 1.732, so 2 is between √3 and 6
The answer is clearly C, since 1.5 is not between √3 and 6
To determine which rational number is not between the square root of 3 and the square root of 6, we can compare each rational number to the square roots.
The square root of 3 is approximately 1.732.
The square root of 6 is approximately 2.449.
Now, let's analyze each of the given rational numbers:
A. 1.8: 1.8 is between 1.732 and 2.449.
B. √4: The square root of 4 is 2. 2 is between 1.732 and 2.449.
C. 1.5: 1.5 is between 1.732 and 2.449.
D. 2: 2 is not between 1.732 and 2.449.
Therefore, the rational number that is not between the square root of 3 and the square root of 6 is D. 2.
To determine which of the given rational numbers is not between the square root of 3 (√3) and the square root of 6 (√6), we need to compare each number to the square roots.
Let's analyze each option:
A. 1.8: To determine if 1.8 is between √3 and √6, we can check if √3 < 1.8 < √6. By calculating the square roots, we find that √3 ≈ 1.732 and √6 ≈ 2.449. Since 1.732 < 1.8 < 2.449, option A is between the two square roots.
B. √4: Since the square root of 4 (√4) is equal to 2, we can check if √3 < 2 < √6. From the calculations above, √3 ≈ 1.732 and √6 ≈ 2.449, but 2 is not between these two values. Therefore, option B is not between √3 and √6.
C. 1.5: Let's determine if 1.5 is between √3 and √6 by assessing if √3 < 1.5 < √6. From the previous calculations, we know that √3 ≈ 1.732 and √6 ≈ 2.449. However, 1.5 is less than √3 and is not between these two values. Consequently, option C is not between √3 and √6.
D. 2: To determine if 2 is between √3 and √6, we can check if √3 < 2 < √6. From the previous calculations, we know that √3 ≈ 1.732 and √6 ≈ 2.449. Since 1.732 < 2 < 2.449, option D is between √3 and √6.
Therefore, the option that is not between √3 and √6 is B. √4.
The square root of 3 is approximately 1.732, and the square root of 6 is approximately 2.449.
A. 1.8 is between the square root of 3 and the square root of 6: 1.732 < 1.8 < 2.449.
B. The square root of 4 is 2, which is between the square root of 3 and the square root of 6: 1.732 < √4 < 2.449.
C. 1.5 is between the square root of 3 and the square root of 6: 1.732 < 1.5 < 2.449.
D. 2 is not between the square root of 3 and the square root of 6: 1.732 < 2.449 < 2.
Therefore, the rational number that is not between the square root of 3 and the square root of 6 is D. 2.
Sure! Let's go through each option one by one and determine if it falls between the square root of 3 and the square root of 6.
A. Option 1.8:
To check if 1.8 is between the square root of 3 and the square root of 6, we can compare these values:
Square root of 3 ≈ 1.732
Square root of 6 ≈ 2.449
Since 1.732 < 1.8 < 2.449, option A is between the square root of 3 and the square root of 6.
B. Option √4:
To check if the square root of 4 is between the square root of 3 and the square root of 6, we need to compare these values:
Square root of 3 ≈ 1.732
Square root of 6 ≈ 2.449
The square root of 4 is 2. Since 1.732 < 2 < 2.449, option B is between the square root of 3 and the square root of 6.
C. Option 1.5:
To check if 1.5 is between the square root of 3 and the square root of 6, we can compare these values:
Square root of 3 ≈ 1.732
Square root of 6 ≈ 2.449
Since 1.732 < 1.5 < 2.449, option C is between the square root of 3 and the square root of 6.
D. Option 2:
To check if 2 is between the square root of 3 and the square root of 6, we compare these values:
Square root of 3 ≈ 1.732
Square root of 6 ≈ 2.449
We have 1.732 < 2.449 < 2. Since 2.449 is larger than 2, option D is not between the square root of 3 and the square root of 6.
Therefore, the rational number that is not between the square root of 3 and the square root of 6 is option D, which is 2.
Apologies for the earlier mistake. You are correct.
The square root of 3 is approximately 1.732, and the square root of 6 is approximately 2.449.
Comparing the values:
1.732 < 1.5 < 2.449
Since 1.5 is not between the square root of 3 and the square root of 6, the correct answer is C.