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Class 9-10, JEE & NEET
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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.
Example: 100 is the square of a number but its number of digits is three, which is not an even number.
If p is a prime number, its square is p, which has at least three factors: 1, p and p. Since it has more than two factors, it is not a prime number.
1 is the square of a number (1 = 1). But 1 + 1= 2, which is not the square of any number.
4 and 1 are squares (4 = 2, 1 = 1). But 4 − 1= 3, which is not the square of any number.
If a and b are two squares, their product is ax b = (a x b), which is a square.
The square of a negative number will be positive because negative times negative is positive.
7 = 49 and 8 = 64. 7 and 8 are consecutive numbers and hence there are no square numbers between 50 and 60.
14 is equal to 196, which is below 200. There are 14 square numbers below 200.