Solution: Square both sides: $ a + 5 = 49 $. Subtract 5: $ a = 44 $. Verify by substituting back: $ \sqrt{44 + 5} = \sqrt{49} = 7 $. Final answer: $ oxed{44} $.

["Solution: Solve $ a + 5 = 49 $ by Squaring Both Sides and Verifying", "When solving simple linear equations involving square roots, it’s often helpful to eliminate the radical by squaring both sides — a powerful algebraic technique. In this article, we’ll walk through how to solve the equation $ a + 5 = 49 $ using squaring, verify the result, and confidently conclude with the final answer.", "---", "### Step 1: Solve the Equation by Isolating the Variable", "We start with the original equation:\n$$\na + 5 = 49\n$$\nTo isolate $ a $, subtract 5 from both sides:\n$$\na = 49 - 5\n$$\n$$\na = 44\n$$", "This gives a direct solution. However, to apply the squaring both sides technique, suppose we were given a root equation that required this step.", "---", "### Step 2: Rewrite as a Root Equation", "Suppose the problem stemmed from:\n$$\n\sqrt{a + 5} = 7\n$$\nTo remove the square root, square both sides:\n$$\n(\sqrt{a + 5})^2 = 7^2\n$$\n$$\na + 5 = 49\n$$", "This matches our initial equation — confirming the reasoning is valid.", "---", "### Step 3: Substitute Back to Verify the Solution", "Now that we have $ a = 44 $, substitute it back into the original expression to verify:\n$$\n\sqrt{44 + 5} = \sqrt{49} = 7\n$$\nSince $ 7 = 7 $, the solution is correct and verified.", "---", "### Step 4: Final Answer", "The accurate and verified solution to the equation is:\n$$\n\boxed{44}\n$$", "---", "### Why This Technique Matters", "Using squaring to eliminate square roots simplifies solving equations that involve irrational expressions. It ensures your work is rigorous and your answer is correct — especially in more complex problems with nested radicals.", "Take control of your algebra: Square wisely, verify thoroughly, and always check your solution."]