Question

4 digit number has the following properties
it is a perfect square
its first two digits are equal to each other
its last two digit are equal to each other
find all such four digit number​

Answer 1

Answer:

7744 is the only number.

Step-by-step explanation:

Let's call first two digits 100a+10a.

It is same as 110a.

Same for last two digits, 11b.

Their sum is 11(10a+b), and it's square number.

So the number is 11k, k are naturals.

starting from $k=2^2*11$

The value is 484, false.

$k=3^3*11$

1089, false

$k=4^2*11$

1936, false

$k=5^2*11$

3025, false

$k=6^2*11$

4536, false

$k=7^2*11$

5929, false

$k=8^2*11$

7744, TRUE

$k=9^2*11$

9801, false