5. Show that 12 is not a square number. Use a diagram, mathematical symbols and then a word sentence.

if y=x^2 the x and y chart would be as follows

x      y

1       1

2      4

3      9

x       12

4      16

5      25

This shows that the x which would produce twelve is between three and 4 and thus not a perfect square

9<12<15 thus 3<x<4

12 is not a perfect square because the square of 3 is 9 and the square of 4 is 16, and since 12 lies between 3 and 4, we know that the number that would be squared to produce twelve must be a decimal between 3 and 4.

Step-by-step explanation:

A perfect square is a number that can be produced from squaring a counting number (...-3,-2,-1,0,1,2,3...)

This means that determining a perfect square comes down to knowing the squares of 1-10 so that you can create a table and determine where the number lies or between what numbers it would occur. If it is a perfect square it will already be on the table with little to no analysis necessary.