Example Card: Isolating the Radical First
Isolate the radical expression on one side before squaring both sides to solve radical equations. Practice Grade 9 radical equation-solving step by step.
Key Concepts
Before you can undo the square root, you must first get it to stand alone. This example illustrates a key idea from the lesson: isolating the radical.
Example Problem Solve the equation $\sqrt{x} 3 = 9$.
Step by Step 1. To solve for $x$, we first need to isolate the radical term, $\sqrt{x}$. 2. Use the Addition Property of Equality. Add $3$ to both sides of the equation. $$ \begin{align } \sqrt{x} 3 &= 9 \\ +3 &= +3 \end{align } $$ 3. Simplify to isolate the radical. $$ \sqrt{x} = 12 $$ 4. Now, use the inverse operation of a square root, which is squaring. Square both sides of the equation. $$ (\sqrt{x})^2 = 12^2 $$ 5. Simplify to find the solution. $$ x = 144 $$ 6. Finally, check the answer by substituting it back into the original equation. $$ \begin{align } \sqrt{144} 3 &\stackrel{?}{=} 9 \\ 12 3 &\stackrel{?}{=} 9 \\ 9 &= 9 \quad \checkmark \end{align } $$.
Common Questions
What is Isolating the Radical First in Grade 9 algebra?
It is a core concept in Grade 9 algebra that builds problem-solving skills and prepares students for advanced math coursework.
How do you apply isolating the radical first to solve problems?
Identify the relevant formula or property, substitute known values carefully, apply each step in order, and verify the result makes sense.
What common errors occur with isolating the radical first?
Misapplying the rule to wrong scenarios, sign mistakes, and forgetting to check answers in the original problem.