Question

If a four-digit perfect square number is such that the number formed by the first two digits and the number formed by the last two digits are also perfect squares, identify the four digit number.

• A. $6416$
• B. $3616$
• C. $1681$
• D. $1664$

Answer 1

The correct option is C $1681$

Four digit number $accd$

$ab$ is a perfect square

$cd$ is also a perfect square

Consider $6416$

$64$and$16$ are perfect square but $6416$ is not a perfect square.

Consider $3616$

$36$and$16$ are perfect square but $3616$ is not a perfect square.

Consider $1681$

$16$and$81$ are perfect square and $1681$ is a perfect square.

Consider $1664$

$16$and$64$ are perfect square but $1664$ is not a perfect square.

Hence, Option C is correct.