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

$10^{2}=100$, or

$10\times 10=100$ that is, 10 to the second power has two zeros after the 1.

Everybody is born to

$2^{1}$ biological parents. Our parents each had

$2^{1}+2^{1}$ biological parents. We can say that our grandparents are

$2^{2}$ 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

$4^{2}=16$ is too small

$5^{2}=25$ is in the range

$6^{2}=36$ is in the range

$7^{2}=49$ is too large

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