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.
(i) The given statement is False
As, the number of digits in a square can also be odd
e.g.: 121
(ii) The given statement is False
As, 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) The given statement is False
Let us take an example:
4 + 9 = 13
As, 4 and 9 are perfect squares of 2 and 3 respectively and their sum i.e., 13 is not a perfect square
(iv) The given statement is also False
Let us take an example:
36 – 25 = 11
As, 36 and 25 are perfect squares and their difference is 11 which is not a perfect square
(v) The given statement is True