Which of the following is an irrational number between 4 and 8?
A. √5
B. √8
C. √17
D. √12
5 answers
C. √17
Can you give an explanation?
Yes, I can provide an explanation.
An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers.
Option A, √5, is an irrational number, but it is less than 4.
Option B, √8, is a rational number because it can be simplified to 2√2.
Option C, √17, is an irrational number and it lies between 4 and 8.
Option D, √12, is a rational number because it simplifies to 2√3.
Therefore, the correct answer is C. √17
An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers.
Option A, √5, is an irrational number, but it is less than 4.
Option B, √8, is a rational number because it can be simplified to 2√2.
Option C, √17, is an irrational number and it lies between 4 and 8.
Option D, √12, is a rational number because it simplifies to 2√3.
Therefore, the correct answer is C. √17
what convoluted logic!
√8 = 2√2 is not rational, since √2 is irrational.
√17 is the answer, since √17 = 4.123, so clearly,
4 < √17 < 8
ones like option D can be checked by looking at the perfect squares, since √x < √y if x < y. Thus,
since 12 < 4^2 < 8^2, we have √12 < 4 < 8
so, you got the right answer, but it's not very satisfying, nor justified.
√8 = 2√2 is not rational, since √2 is irrational.
√17 is the answer, since √17 = 4.123, so clearly,
4 < √17 < 8
ones like option D can be checked by looking at the perfect squares, since √x < √y if x < y. Thus,
since 12 < 4^2 < 8^2, we have √12 < 4 < 8
so, you got the right answer, but it's not very satisfying, nor justified.
You are correct, and I apologize for the confusing explanation I provided earlier. Your explanation is much clearer and more accurate.
√8 cannot be expressed as a fraction or a ratio of two integers since it involves the irrational number √2.
√17, on the other hand, is an irrational number that lies between 4 and 8. By calculating its approximate value, we can see that 4 < √17 < 8.
Thank you for pointing out the errors in my previous response, and I appreciate your feedback.
√8 cannot be expressed as a fraction or a ratio of two integers since it involves the irrational number √2.
√17, on the other hand, is an irrational number that lies between 4 and 8. By calculating its approximate value, we can see that 4 < √17 < 8.
Thank you for pointing out the errors in my previous response, and I appreciate your feedback.