Radical Equation
Solve radical equations in Grade 9 Algebra by isolating the radical and squaring both sides. Always check solutions to identify and reject extraneous roots.
Key Concepts
Property An equation containing a variable trapped inside a radicand, like $\sqrt{x} = 9$. Explanation To solve these puzzles, you must free the variable! The main move is to square both sides of the equation. This is the inverse operation that undoes the square root, allowing you to find the value of the variable. Examples Solve $\sqrt{x} = 8$. Square both sides: $(\sqrt{x})^2 = 8^2$, so $x=64$. Solve $\sqrt{x+3} = 5$. Square both sides: $x+3 = 25$, so $x=22$.
Common Questions
How do you solve a radical equation step by step?
Isolate the radical expression on one side of the equation, then square both sides to eliminate the radical. Solve the resulting equation and always substitute your answers back into the original to check for extraneous solutions.
What is an extraneous solution in a radical equation?
An extraneous solution is a value that satisfies the squared equation but not the original radical equation. It appears because squaring can introduce false solutions. Always verify each answer in the original equation to reject extraneous roots.
Why must you check solutions after solving radical equations?
Squaring both sides is not a reversible step—it can create solutions that work in the squared form but violate the original. Substituting back into the original radical equation is the only reliable way to confirm validity.