Question

Which of the following statements is always true:

a) A square number cannot be the sum of two other square numbers.

b) A number that has 5 in the units place can never be a perfect square.

c) A number that leaves a remainder of 3 when divided by 4 cannot be a perfect square

d) A number that has 7 in the units place may be a perfect square

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Answer 1

Answer:

1st

Step-by-step explanation:

Answer 2

Answer:

The true statement is: c) A number that leaves a remainder of 3 when divided by 4 cannot be a perfect square.

Step-by-step explanation:

All the points are discussed below to prove whether they are true or false:

a) Suppose a square number is 16, which is the square of 4.

  Another square number is 9, which is square of 3.

The sum of them = 16 + 9 = 25, which is the square of 5.

So, the statement- "A square number cannot be the sum of two other square numbers" - is false.

b) In the number 25, 5 is in the unit place.

   And also 25 = 5² . 25 is a perfect square.

So, the statement- "A number that has 5 in the units place can never be a perfect square" - is false.

c) All the perfect squares will either leave a remainder 1 or be a multiple of 4. If any number leave remainder 3, when divided by 4 then the number is not a perfect square.

Example- 7 is a number. when 7 is divided by 4, the remainder = 3. But 7 is not a perfect square.

So, the statement- "A number that leaves a remainder of 3 when divided by 4 cannot be a perfect square" - is true.

d) There is no perfect square that has 7 at unit place. So, the 4th statement is false.

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