Question

Why is√5 irrational?
A.)because it is less than one
B.)because it has no opposite
C.)because all square roots are irrational
D.)because it cannot be expressed as a ratio of integers

Answer 1

Answer: The expression x(x + 1) is even for any integer x (since either x or x + 1 is even). So this says that 5 × even + 1 = even, or odd = even. Since there is no integer that is both even and odd, we have reached a contradiction and √5 is irrational. So the answer would be D.) because it cannot be expressed as a ratio of integers