**The missing number in the following series: 9, ____, 6561, 43046721 is clearly 81.**

Here's how I worked it out:

Nine multiplied by nine equals 81. 81 multiplied by 81 equals 6561, and 6561 multiplied by 6561 equals 43046721. The mathematical equation used for this type of sum is called squared. This means multiplying a number by itself. The opposite of a squared number is a square root. A square root is a mathematical equation that is difficult to achieve unless the number is divisible wholly by itself.

In this case the square root of 81 is nine as is it divisible by itself. However, to obtain the square root of 20 needs some guesswork. This is because 20 is not divisible by itself. We know that the square root of 16 will be four, as four multiplied by four is 16. We also know that the square root of 25 is five, as five multiplied by five is 25.

To obtain the square root of 20 we would need to guess and the best place to start would be in the middle of the previous two calculations, so we could start at 4.5. 4.5 multiplied by 4.5 equals 20.25, so that is pretty close. We could by attempt a lower number to become more accurate, for example, 4.48 multiplied by 4.48 equals 20.07. This can then be worked out by adding digits after the decimal point until the answer is achieved. The nearest you can get for this particular sum is to multiply 4.472 by itself, which will give the answer as 19.998.