Write true (T) or false (F) for the following statements.

Solution:

(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.