To solve the equation \((x + 3)^2 = 36\) using square roots, follow these steps:
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Take the square root of both sides: \[ x + 3 = \pm 6 \]
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Solve for \(x\) by considering both the positive and negative cases:
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Case 1: \[ x + 3 = 6 \] Subtracting 3 from both sides gives: \[ x = 6 - 3 = 3 \]
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Case 2: \[ x + 3 = -6 \] Subtracting 3 from both sides gives: \[ x = -6 - 3 = -9 \]
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Therefore, the solutions to the equation \((x + 3)^2 = 36\) are: \[ x = 3 \quad \text{and} \quad x = -9 \]
So, the final answers are \(x = 3\) and \(x = -9\).
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