91Ó°ÊÓ

A square root of a number is a value that, when multiplied by itself, gives the original number. For instance, the square root of 9 is 3 because \(3 \times 3 = 9\). In this exercise, we are dealing with the square root of 82.
To find the square root of 82, you can use a calculator because it's not a perfect square (a whole number). So, we get an approximation instead. Entering 82 into your calculator and finding its square root gives about 9.055. This means \(9.055 \times 9.055 \approx 82\).
Always remember, square roots can be positive or negative. But in our case, we are looking at the negative square root.

Negative numbers are numbers that are less than zero. They have a minus sign in front of them, for example, -3.
When we talk about applying a negative sign in mathematics, it simply means we are taking the value and making it negative. Since the original question is \( -\sqrt{82} \), after finding \( \sqrt{82} \approx 9.055 \), we apply the negative sign to get -9.055. This changes the direction of the number on the number line.
Working with negative numbers is straightforward: just keep in mind that they are below zero. For example, if you owe \(5 (which is -5) and borrow another \)10 (which is another -10), you owe $15 in total (which is -15).

Calculators are useful tools in mathematics. They can speed up calculations and reduce human error. When you're trying to find the square root of a non-perfect square like 82, it's practical to use a calculator to get an accurate answer.
To use a calculator for finding a square root, enter the number (in this case, 82) and press the square root button. You'll get the approximate result, which is about 9.055. Make sure your calculator is in the correct mode (usually degree mode for general calculations).
Calculators handle complex operations easily and quickly. They're especially helpful in exams or homework when you need precise values or when dealing with large numbers. Just be cautious: always double-check to ensure you entered everything correctly and review the result to ensure it makes sense.