Hi.
for a square root equation with variables such as x or y, when do u need the absolute value sign?
Im kinda confused and my teacher didn't go over it.
Help please?
thanks
skye!
Unless otherwise directed, I would not use the absolute value sign.
Hi Skye! Great question. When dealing with square root equations involving variables like x or y, there are certain situations where you may need to use the absolute value sign.
The absolute value sign, denoted by two vertical lines ||, is used to ensure that the square root equation remains positive, even when the expression inside the square root could potentially be negative.
Here are a few cases where you would need to use the absolute value sign:
1. When taking the square root of a variable squared:
If you have an equation like √(x^2) = y, you would need to use the absolute value sign around the variable x, like this: |x|.
This is because x^2 can be positive or negative, and taking the square root of a negative number is not possible in real numbers. By using the absolute value sign, you make sure that x remains positive, so the equation is solvable.
2. When the expression inside the square root can potentially be negative:
For example, if you have an equation like √(x - 5) = y, the expression (x - 5) can be negative if x < 5. In this case, you would need to use the absolute value sign around the expression, like this: |x - 5|. This guarantees that the expression inside the square root is always positive, allowing you to solve the equation.
Remember, the absolute value sign is not always necessary in square root equations. It only comes into play when there is a possibility of the expression inside the square root being negative.
I hope this clears up your confusion! Let me know if there's anything else I can help you with.