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.