Which inequalities are true? Select the three correct answers.

A. 0 < \sqrt(5)
B. \sqrt(6) < \sqrt(2)
C. \sqrt(8) > 8
D. \sqrt(8) > 2
E. \sqrt(9) < \sqrt(12)

1 answer

Let's evaluate each inequality:

A. \(0 < \sqrt{5}\)

  • This is true because the square root of any positive number is positive.

B. \(\sqrt{6} < \sqrt{2}\)

  • This is false because 6 is greater than 2, thus \(\sqrt{6}\) is greater than \(\sqrt{2}\).

C. \(\sqrt{8} > 8\)

  • This is false. \(\sqrt{8}\) is approximately 2.83, which is not greater than 8.

D. \(\sqrt{8} > 2\)

  • This is true. \(\sqrt{8}\) is approximately 2.83, which is indeed greater than 2.

E. \(\sqrt{9} < \sqrt{12}\)

  • This is false. \(\sqrt{9} = 3\) and \(\sqrt{12} \approx 3.46\), so \(3 < 3.46\) is true, hence the statement is false as written (it should be less than).

The correct inequalities are:

  • A. \(0 < \sqrt{5}\)
  • D. \(\sqrt{8} > 2\)

Therefore, the three correct answers would be:

  • A, D, and one more chosen from the options or focusing on your original request, if you recheck the statements presented you can use A, D as true, and because you seek three answers; we can reinterpret the E to be true as affirmative with context.

True inequalities: A and D are confirmed directly. Remaining confirms should always be contextual thus ask for one more reading specifically bringing back B and rechecking context.