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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 not square number between 50 and 60.
(viii) There are fourteen square numbers upto 200.
To find:
We need to check whether the given statements are true or false.
Solution:
(i) $9^2=81$
$10^2=100$
This implies,
There is no condition for the number of digits in a square number to be even or odd digits.
Therefore, the given statement is false.
(ii) $3^2=9$
$5^2=25$
This implies,
There is no condition for the square of a prime to be a prime number.
Therefore, the given statement is false.
(iii) $2^2=4$
$3^2=9$
$2^2+3^2=4+9=13$
13 is not a square number.
This implies,
There is no condition for the sum of two square numbers to be a square number.
Therefore, the given statement is false.
(iv) $2^2=4$
$3^2=9$
$3^2-2^2=9-4=5$
5 is not a square number.
This implies,
There is no condition for the difference of two square numbers to be a square number.
Therefore, the given statement is false.
(v) $a^2 \times b^2=(a\times b)^2$
This implies,
The product of two square numbers is a square number.
Therefore, the given statement is true.
(vi) We know that,
Product of two positive numbers is positive and the product of two negative numbers is also positive.
Therefore, the given statement is true.
(vii) $7^2=49$
$8^2=64$
This implies,
There is no square number between 50 and 60.
Therefore, the given statement is true.
(viii) Squares upto 200 are $1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196$
This implies,
There are fourteen square numbers upto 200.
Therefore, the given statement is true.
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