Question

Let
represent a non-zero rational number and let
represent an irrational number.

Part A
Which expression could represent a rational number?​
A
−b{}^{-}{b}{}
−
b
B
a+ba+ba+b
C
ababab
D
b2b^{2}b
2

Answer 1

D. b^2

Reason: An irrational number squared can be rational (for example, if b = √2 then b^2 = 2, which is rational). By contrast, sums or nonzero rational multiples of an irrational are always irrational (e.g. a + b and a·b are irrational when a ≠ 0), so the other choices cannot yield a rational number.