Calculating powers of 10 become easier when understanding that the exponent gives a clue to how many zeros there are after the 1.

For example, ${\displaystyle 10^{1}=10}$, that is, 10 to the first power has one zero after the 1.

${\displaystyle 10^{2}=100}$, or ${\displaystyle 10\times 10=100}$ that is, 10 to the second power has two zeros after the 1.

Everybody is born to ${\displaystyle 2^{1}}$ biological parents. Our parents each had ${\displaystyle 2^{1}+2^{1}}$ biological parents. We can say that our grandparents are ${\displaystyle 2^{2}}$ mathematically as the number of our ancestors doubles with each generation we go back.
So:

We can identify the square numbers between two numbers by simply squaring basic numbers. For example:

To identify the square numbers between 20 and 40 we can say
${\displaystyle 4^{2}=16}$ is too small
${\displaystyle 5^{2}=25}$ is in the range
${\displaystyle 6^{2}=36}$ is in the range
${\displaystyle 7^{2}=49}$ is too large

So the square numbers in that range are 5 and 6.