(2) Which of the following numbers is irrational?
(A) 45.8
(B) \( \sqrt{50} \)
(C) \( \sqrt{100} \)
(D) \( 0.1 \overline{6} \)

Answer

Expert–verified

Hide Steps

Answer

Thus, \( \sqrt{50} \) is the irrational number.

Steps

Step 1 ：Check if each option results in a non-terminating, non-repeating decimal:

Step 2 ：45.8 is a terminating decimal, eliminating (A)

Step 3 ：\( \sqrt{100} = 10 \), a rational number, eliminating (C)

Step 4 ：0.1\overline{6}=\( \frac{1}{6} \) comes to a repeating decimal, eliminating (D)

Step 5 ：Thus, \( \sqrt{50} \) is the irrational number.