Question

Write true (T) or false (F) for the following statements.
(i) The number of digits in a square number is even.
(ii) The square of a prime number is prime.
(iii) The sum of two square numbers is a square number.
(iv) The difference of two square numbers is a square number.
(v) The product of two square numbers is a square number.
(vi) No square number is negative.
(vii) There is no square number between 50 and 60.
(viii) There are fourteen square number upto 200.

Answer 1

(i) False
Example: 100 is the square of a number but its number of digits is three, which is not an even number.

(ii) False
If p is a prime number, its square is p², which has at least three factors: 1, p and p². Since it has more than two factors, it is not a prime number.

(iii) False
1 is the square of a number (1 = 1²). But 1 + 1 = 2, which is not the square of any number.

(iv) False
4 and 1 are squares (4 = 2², 1 = 1²). But 4 − 1 = 3, which is not the square of any number.

(v) True
If a² and b² are two squares, their product is a² x b² = (a x b)², which is a square.

(vi) True
The square of a negative number will be positive because negative times negative is positive.

(vii) True
7² = 49 and 8² = 64. 7 and 8 are consecutive numbers and hence there are no square numbers between 50 and 60.

(viii) True
14² is equal to 196, which is below 200. There are 14 square numbers below 200.