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.

The correct option is (d) only.

Let us analyze each statement step-by-step to determine whether it is true or false.

Statement (a): A number never exceeds its square.
Let the number be $x$.
If we choose $x=0.5$, its square is:
$x^2={\left(0.5\right)}^2=0.25$
Here, $0.5>0.25$, which means the number exceeds its square.
Therefore, statement (a) is false.

Statement (b): All negative numbers exceed their cubes.
Let $x$ be a negative number.
If we choose $x=-2$, its cube is:
$x^3={(-2)}^3=-8$
Since $-2>-8$, the number $-2$ exceeds its cube.
However, if we choose a negative fraction like $x=-0.5$, its cube is:
$x^3={(-0.5)}^3=-0.125$
Since $-0.5<-0.125$, the number $-0.5$ is smaller than its cube.
Thus, not all negative numbers exceed their cubes.
Therefore, statement (b) is false.

Statement (c): A number never exceeds its cube.
As shown above, for $x=2$, $x^3=8$ ($2<8$), but for $x=-2$, $x^3=-8$ ($-2>-8$).
Also, for $x=0.5$, $x^3=0.125$ ($0.5>0.125$).
Here, the number exceeds its cube.
Therefore, statement (c) is false.

Statement (d): The square root of a prime number is not a rational number.
A prime number has no factors other than 1 and itself, so it cannot be expressed as a square of any rational number.
Hence, the square root of any prime number (such as $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$) is an irrational number (i.e., not a rational number).
Therefore, statement (d) is true.

Thus, statement (d) is the only true statement, which corresponds to option (d) only.