Final answer:
The symbolic representation of 'When you square five times a number, you get three more than the number' is (5x)^2 = x + 3.
Step-by-step explanation:
To write the statement 'When you square five times a number, you get three more than the number' symbolically, you first need to identify the variable, which in this case will represent 'a number.'
Let's use x as our variable. Now, 'five times a number' can be represented as 5x, and 'when you square' this quantity, it becomes (5x)^2.
Finally, 'you get three more than the number' translates to x + 3.
Combining these, the complete symbolic statement is (5x)^2 = x + 3.
Squaring a number is the mathematical shorthand for multiplying that number by itself. When an exponent is applied to a product like 5x, it affects both terms, so (5x)^2 means 5x multiplied by 5x.
To resolve such equations, standard algebraic manipulations and the reverse operations of squaring, such as taking square roots, are used to find the value of the variable.