Final answer:
The mathematical statement "The quotient of the square of a number and 3 exceeds the square root of the product of the number and 9" can be expressed as the inequality ²/3 > (9x)¹⁰⁵.
Step-by-step explanation:
To express the mathematical statement "The quotient of the square of a number and 3 exceeds the square root of the product of the number and 9," let us define the variable x as the number in question. The statement involves two main operations: squaring and finding a quotient, as well as taking a square root and finding a product. Squaring a number x is expressed as x², and the quotient of that square by 3 is x²/3. On the other side of the statement, finding the square root can be expressed as the fractional exponent ½, and the product of the number and 9 is 9x. Putting this together, the square root of the product of the number and 9 is (9x)¹⁰⁵. The original statement can now be written as an inequality: x²/3 > (9x)¹⁰⁵