Final answer:
The positive number that, when 5 is added to it and squared, gives 81 is 4. We solved the equation (x + 5)² = 81 by taking the square root of both sides and subtracting 5 from 9.
Step-by-step explanation:
When we add 5 to a certain positive number and square the result to get 81, we are effectively solving the equation (x + 5)² = 81. To find the number, we need to take the square root of both sides to eliminate the exponent. Square roots take us back to the base number that was squared. So, the square root of 81 is 9, meaning (x + 5) must equal either 9 or -9. Since we are given that the number is positive, we only consider x + 5 = 9.
To isolate the variable x, we subtract 5 from both sides and find that x = 4. This is our positive number that solves the equation. Hence, when 5 is added to 4 and the result is squared, it indeed equals 81.