Match each equation in Column I with the correct first step for solving it in Column II. √(x+5) = 7

Verified step by step guidance

1. Identify the equation given: \(\sqrt{\\(x+5\")} = 7\).
2. Recognize that the square root is isolated on one side of the equation, which allows us to eliminate the square root by squaring both sides.
3. Square both sides of the equation to remove the square root: \(\left(\sqrt{\\(x+5\")}\right)^2 = 7^2\).
4. Simplify both sides after squaring: \(x + 5 = 49\).
5. Proceed to solve the resulting linear equation by isolating \(x\): subtract 5 from both sides to get \(x = 49 - 5\).

Key Concepts

Square Root Property

The square root property involves understanding that if √A = B, then A = B². This is essential for solving equations with square roots, as it allows you to eliminate the radical by squaring both sides, simplifying the equation to a polynomial form.

Isolating the Radical Expression

Before applying the square root property, the radical expression must be isolated on one side of the equation. This ensures that squaring both sides will correctly remove the square root without introducing extraneous terms or complicating the equation.

Checking for Extraneous Solutions

Squaring both sides of an equation can introduce solutions that do not satisfy the original equation. After solving, it is important to substitute solutions back into the original equation to verify their validity and discard any extraneous solutions.