91Ó°ÊÓ

When solving radical equations, the first crucial step is isolating the variable. This means we need to get the term containing the variable alone on one side of the equation. Let’s take a look at our example:
In the equation \(3 \sqrt{t} + 10 = 9 \sqrt{t} - 2\), we can identify that the terms involving the variable are \(3 \sqrt{t}\) and \(9 \sqrt{t} \). To isolate the term with the variable, we subtract \(3 \sqrt{t}\) from both sides:
\(3 \sqrt{t} + 10 - 3 \sqrt{t} = 9 \sqrt{t} - 2 - 3 \sqrt{t} \). This simplifies to \(10 = 6 \sqrt{t} - 2\). Now, we have successfully moved all the variable terms to one side of the equation.
By isolating \(6 \sqrt{t} - 2\), it becomes easier to handle the variable.

After isolating the variable, the next step is simplifying the equation. Simplifying makes it easier to solve by reducing the equation to its simplest form.
Continuing with our isolated equation \(10 = 6 \sqrt{t} - 2 \), we add 2 to both sides to get:
\(10 + 2 = 6 \sqrt{t} \).
This simplifies to \(12 = 6 \sqrt{t} \).
Next, we further simplify by dividing both sides by the coefficient of the square root term (which is 6):
\(\frac{12}{6} = \sqrt{t} \).
So, \(2 = \sqrt{t} \).
Now, our equation is much simpler and ready for the next step, which is solving for the variable.

Understanding square root properties is essential for solving radical equations. A square root essentially