Using rational approximations, which statement is true?
A √48 > √36
B √49 > 7
C √49 < 7
D √48 < √36
I apologize for the confusion in my previous response. There was an error in my explanation.
The correct comparison is √48 > √36. This means that option A: √48 > √36 is the true statement using rational approximations.
Here's the corrected explanation:
Using rational approximations, let's approximate the square roots of 48 and 36:
√48 is approximately equal to √(4 × 12) = √4 × √12 = 2√12.
Similarly, √36 is approximately equal to √(6 × 6) = 6.
Comparing 2√12 and 6, we see that 2√12 is greater than 6.
Therefore, √48 is greater than √36.
So, by using rational approximations, the statement √48 > √36 is true. The correct answer is A: √48 > √36.
how did you say that √48 > √36 but then say that D. √48 < √36 is right?
Using rational approximations, what statement is true?(1 point)
√71 > √61
√81 < 9
√71 < √61
√81 > √9
Using rational approximations, the statement √81 < 9 is true, which means option B: √81 < 9 is the correct statement.
To understand why, let's look at the square roots of 81 and 9:
√81 is equal to 9.
Similarly, √9 is equal to 3.
Comparing 9 and 3, we see that 9 is greater than 3.
Therefore, √81 is greater than √9.
However, options A, C, and D are not true when using rational approximations:
- √71 is approximately equal to 8.4, while √61 is approximately equal to 7.8. Therefore, option A: √71 > √61 is not true.
- √71 is greater than √61, so option C: √71 < √61 is not true.
- As mentioned earlier, comparing 9 and 3, we see that 9 is greater than 3. Therefore, option D: √81 > √9 is not true.
So, the correct statement using rational approximations is √81 < 9.
wait sorry the 9's weren't supposed to have √
My apologies for the confusion. Without the square root symbol, the correct statement is:
√81 > 9
Using rational approximations, we can approximate the square root of 81 as follows:
√81 is approximately equal to √(9 × 9) = 9.
Comparing 9 and 9, we see that they are equal.
Therefore, √81 is equal to 9, and √81 is greater than 9.
So, the correct statement using rational approximations is √81 > 9. The correct option is D: √81 > √9.
thank you and once again sorry about the confusion
No problem at all! I'm here to help clarify any confusion and provide accurate information. If you have any more questions, feel free to ask.
To determine which statement is true using rational approximations, we need to find the approximate values of the square roots involved and compare them.
Let's first find the approximate value for √48:
We can approximate the square root of 48 by finding the perfect squares closest to it. The perfect square smaller than 48 is 36 (which is 6²), and the perfect square larger than 48 is 49 (which is 7²). Since 48 is closer to 49 than 36, we can approximate √48 as slightly less than 7.
Using the same approach, let's find the approximate value for √36:
The perfect square smaller than 36 is 36 itself (which is 6²). Since 36 is already a perfect square, √36 equals 6.
Now, let's compare the approximations:
A: √48 > √36
Approximation of √48: slightly less than 7
Approximation of √36: 6
Since slightly less than 7 is greater than 6, the statement A is true.
B: √49 > 7
Approximation of √49: 7
Since 7 is equal to 7, the statement B is false.
C: √49 < 7
Approximation of √49: 7
Since 7 is equal to 7, the statement C is false.
D: √48 < √36
Approximation of √48: slightly less than 7
Approximation of √36: 6
Since slightly less than 7 is greater than 6, the statement D is false.
In conclusion, the only true statement is A: √48 > √36.
Using rational approximations, the statement D √48 < √36 is true.
To see why, let's look at the square roots of 48 and 36:
√48 is approximately equal to √(4 × 12) = √4 × √12 = 2√12.
Similarly, √36 is approximately equal to √(4 × 9) = √4 × √9 = 2√9.
Now let's compare 2√12 and 2√9:
Since 12 is greater than 9, √12 is greater than √9.
Therefore, 2√12 is greater than 2√9, or √48 is greater than √36.
So, by using rational approximations, the statement √48 < √36 is true. The correct answer is D √48 < √36.