a. \( x^{\frac{1}{2}}=3 \)

To solve the equation: \[ x^{\frac{1}{2}} = 3 \] follow these steps: ### Step 1: Understand the Equation The expression \( x^{\frac{1}{2}} \) is equivalent to the square root of \( x \). So, the equation can be rewritten as: \[ \sqrt{x} = 3 \] ### Step 2: Eliminate the Square Root To solve for \( x \), square both sides of the equation to eliminate the square root: \[ \left( \sqrt{x} \right)^2 = 3^2 \] \[ x = 9 \] ### Step 3: Verify the Solution It's always good practice to verify the solution by substituting it back into the original equation: \[ x^{\frac{1}{2}} = 3 \quad \Rightarrow \quad 9^{\frac{1}{2}} = 3 \] \[ \sqrt{9} = 3 \quad \Rightarrow \quad 3 = 3 \quad \text{✓} \] The solution satisfies the original equation. ### **Solution:** \[ x = 9 \]