Isolating the Square Root
Isolate the square root in Grade 9 algebra equations. Get the radical alone before squaring both sides, solve the resulting equation, and check for extraneous solutions.
Key Concepts
Property The radical must be isolated on one side of the equation before squaring. Explanation To solve, get the radical by itself! Use inverse operations to move other numbers away. Once it is alone, you can square both sides of the equation. This removes the root and makes solving simple. Examples Solve $\sqrt{x} + 5 = 9$. Subtract 5: $\sqrt{x}=4$. Then square to get $x=16$. Solve $4\sqrt{x} = 20$. Divide by 4: $\sqrt{x}=5$. Then square to get $x=25$.
Common Questions
How do you isolate a square root before solving?
Move all non-radical terms to the other side using inverse operations. Get the square root expression alone on one side before squaring to remove the radical.
What are the steps to solve an equation with a square root?
1. Isolate the square root. 2. Square both sides. 3. Solve the resulting equation. 4. Substitute back into the original to check for extraneous solutions.
Why must you check solutions to radical equations?
Squaring both sides can introduce extraneous solutions — values that work in the squared equation but not the original. Always substitute back into the original radical equation.