Question

5. Determine whether the statements are always, sometimes, or never true. If a statement is always true or always false, explain why. If it is sometimes true, give an example of when it is true and when it is not true.
(a) The square of a rational number is a rational number.
(b) The square of an irrational number is an irrational number.
(c) The square root of a rational number is a rational number.
(d) The square root of an irrational number is an irrational number.

Answer 1

a.
let q be a rational number st q = a/b, a/b are elements of Z, then
q^2 = (a/b)^2 = a^2/b^2
let c = a^2, c is an element of z
let d = b^2, d is an element of z

q^2 = c/d
q^2 is a rational number

Answer 2

what is the number?

Answer 3

what