The sum of two perfect squares is a perfect square.

True

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False

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Sometimes

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Never

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Solution

The correct option is C Sometimes
The given statement is sometimes true and sometimes it is false.

Example:
$6^{2} + 5^{2} = 36 + 25$
$= 61$
which is not a square number so, here it is false.

But, $3^{2} + 4^{2} = 9 + 16$
$= 25$
which is perfect square of $5$ so, here it is true.

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Question 50

State whether the following statement is true or false:

The sum of two perfect squares is a perfect square.

(Exploration) Find all perfect squares from 1 to 500, each of which is a sum of two perfect squares.

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