Question

To get the echo of a positive integer, we write it twice in a row without a space. For example, the echo of 2022 is 20222022. Is there a positive integer whose echo is a perfect square

Answer 1

The echo number 20222022202220222022 is the perfect square of 4496890281.

What echo number is a perfect square

An echo number has a perfect square if its square root is also a natural number. After some iterations we found that echo number 20222022202220222022 is a perfect square:

$\sqrt{20222022202220222022} = 4496890281$

The echo number 20222022202220222022 is the perfect square of 4496890281. $\blacksquare$

To learn more on natural numbers, we kindly invite to check this verified question: brainly.com/question/17429689