91Ó°ÊÓ

When solving radical equations, the first step is to isolate the square root expression. For example, in the equation \( \sqrt{6k - 1} = 1 \), the square root term is already isolated. This means that the square root part of the expression is alone on one side of the equation.
Isolating the square root simplifies the next steps because it makes the equation easier to manipulate.
If the square root term is not isolated, move other terms to the opposite side using basic algebraic operations such as addition or subtraction.
Make sure no constants or other expressions are attached to the square root term, either through addition, subtraction, or multiplication. By isolating the square root, you set yourself up for the next step: squaring both sides.

Once the square root is isolated, you need to eliminate it by squaring both sides of the equation. Squaring is the inverse operation of taking the square root.
Let's apply this to our example. We started with: \[ \sqrt{6k - 1} = 1 \].
To remove the square root, we square both sides of the equation:
\[ (\sqrt{6k - 1})^2 = 1^2 \].
Squaring the square root term simplifies to:
\[ 6k - 1 = 1 \].
Remember, when squaring both sides of an equation, always ensure you apply the operation correctly to avoid mistakes. This step transforms a radical equation into a simple linear equation, making the problem easier to solve in the next step.

Now that we've transformed our equation into a linear one, the final step is to solve for the variable. Using our example, we have: \[ 6k - 1 = 1 \].
Start by isolating the variable term. Add 1 to both sides to move the constant term to the right side of the equation: \[ 6k - 1 + 1 = 1 + 1 \], which simplifies to \[ 6k = 2 \].
Next, divide both sides by 6 to isolate \( k \): \[ k = \frac{2}{6} = \frac{1}{3} \].
It's important to check your solution by substituting \( k \) back into the original equation to ensure it satisfies the equation. In this case, substituting \( k = \frac{1}{3} \) back into \[ \sqrt{6k - 1} = 1 \] confirms that our solution is correct. By following these steps, you can confidently solve radical equations.