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What do the numbers in the square with the symbols represent?
Math
Why is square numbers called square numbers?
They are called square numbers because they can form a square and the square is one number times itself. They are called square numbers because they represent the area of a square with integer sidelengths. Example: 49. 49 is the area of a 7x7 square, so 49 is a square number.
Is there a number that doesn't have a square root?
Any negative number, and infinity. However, a number (called "i") was created to represent the square roots of negative numbers.
Could the side lengths 9 15 and 10 represent a right triangle?
No. In order to be the sides of a right triangle, the square of one of the numbers must be the sum of the squares of the other two numbers. (the square of 9) + (the square of 10) = 181 but (the square of 15) = 225 .
What do imaginary numbers represent?
The real numbers together with the imaginary numbers form a sort of vector. What these complex numbers (complex means the combination of real and imaginary numbers) represent depends on the specific situation. Just as there are situations where it doesn't make sense to use negative numbers, or fractional numbers, in many common situations it doesn't make sense to use complex numbers. In an electrical circuit (specifically, AC), the real numbers might represent resistance, while the imaginary number represent reactance - and voltages and currents are also represented by complex numbers, with the angle of the complex number representing how much one quantity is ahead or behind another quantity (the "phase angle"). In quantum mechanics, the complex numbers might not represent anything (perhaps they don't, I am not sure...), but they are useful for calculations.
