Question

if 10^3 A + A is a perfect square then the minimum number of digits in A is ​

Answer 1

A is a 4 digits number.

Step-by-step explanation:

Given that $10^{3} A + A$ is a perfect square

Now, Simply the given equation we get,

$= 10^{3} \times A + A\\\\= 1000 \times A + A\\\\= A (1000 + 1)\\\\= A\times 1001$

Than , $A\times 1001 = 10^{3}\times A + A$

According to question it is a perfect square. As we know that for the perfect square same value is multiply by the same value. For example 16 × 16  where 256 is a perfect square.

Therefor, $A\times 1001 = 1001\times 1001$

∴ $A = 1001$

Hence, The minimum number of digits A is 4.