the product of the square of a number and the cube of the same number is 243. what is this number?

I assume this is what you mean:

 

x^2 + x^3=243, solve for x

x=5.92409131, so that:

5.92409131^2 + 5.92409131^3=~243

X^2*x^3 → x^5

 

x^5 = 243 means x = 3