Solve the equation by extracting square roots. When a solution is irrational, list both the exact solution and its approximation rounded to two dedimal places. (If a solution is rabional, enter fat for ts apporimation.) \[ 4 x^{2}=16 \] smaller value \( \quad x=\square=\square \) larger value \( \quad x=\square \)

Solve the quadratic equation by following steps: - step0: Solve using square roots: \(4x^{2}=16\) - step1: Divide both sides: \(\frac{4x^{2}}{4}=\frac{16}{4}\) - step2: Divide the numbers: \(x^{2}=4\) - step3: Simplify the expression: \(x=\pm \sqrt{4}\) - step4: Simplify the expression: \(x=\pm 2\) - step5: Separate into possible cases: \(\begin{align}&x=2\\&x=-2\end{align}\) - step6: Rewrite: \(x_{1}=-2,x_{2}=2\) To solve the equation \( 4x^{2} = 16 \) by extracting square roots, we can follow these steps: 1. **Isolate \( x^{2} \)**: \[ x^{2} = \frac{16}{4} = 4 \] 2. **Take the square root of both sides**: \[ x = \pm \sqrt{4} \] 3. **Calculate the square roots**: \[ x = -2 \quad \text{and} \quad x = 2 \] Now, we can summarize the solutions: - Smaller value: \( x = -2 \) - Larger value: \( x = 2 \) Since both solutions are rational, their approximations are simply "fat" (indicating they are rational). Thus, the final answers are: - Smaller value \( \quad x = -2 = \text{fat} \) - Larger value \( \quad x = 2 = \text{fat} \)