Discussion
Which of the following statement(s) is/are true ?
(a) A number never exceeds its square.
(b) All negative numbers exceeds their cubes.
(c) A number never exceeds its cube.
(d) The square root of a prime number is not a rational number.
Answer: B
Only statement (d) is true, so the answer is (d) only.
(d) is true: if p is prime, √p cannot be written as a fraction, because p appears to an odd power in any square, so √2, √3 and √5 are all irrational.
The others fail on fractions and negatives. (a) is false: 1/2 exceeds its square 1/4. (b) is false: −1/2 does not exceed its cube −1/8, since −1/8 is greater. (c) is false: 1/2 exceeds its cube 1/8, and −2 exceeds its cube −8. So every option containing (a), (b) or (c) is wrong.
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