Question

Write (T) for true and (F) for false for each of the statements given below:
(i) The number of digits in a perfect square is even.
(ii) The square of a prime number is prime.
(iii) The sum of two perfect squares is a perfect square.
(iv) The difference of two perfect squares is a perfect square.
(v) The product of two perfect squares is a perfect square.

Answer 1

(i) F
The number of digits in a square can also be odd. For example: 121

(ii) F
A prime number is one that is not divisible by any other number, except by itself and 1. Thus, square of any number cannot be a prime number.

(iii) F
Example: $4+9=13$
4 and 9 are perfect squares of 2 and 3, respectively. Their sum (13) is not a perfect square.

(iv) F
Example: $36-25=11$
36 and 25 are perfect squares. Their difference is 11, which is not a perfect square.

(v) T