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, so the first step is to eliminate the square root by squaring both sides.
3. Square both sides of the equation to get rid of the square root: \((\sqrt{(x+5)})^2 = 7^2\).
4. Simplify both sides: \(x + 5 = 49\).
5. Proceed to solve the resulting linear equation by isolating \(x\).

Key Concepts

Square Root and Radicals

A square root of a number is a value that, when multiplied by itself, gives the original number. Radicals involve roots, and understanding how to manipulate them is essential for solving equations like √(x+5) = 7. Recognizing that squaring both sides can eliminate the square root is a key step.

Isolating the Variable

Isolating the variable means rewriting the equation so that the variable stands alone on one side. This often involves performing inverse operations, such as squaring both sides to remove a square root, which simplifies the equation and makes it easier to solve for x.

Solving Quadratic Equations

After removing the square root by squaring both sides, the equation may become quadratic. Understanding how to solve quadratic equations—by factoring, using the quadratic formula, or completing the square—is important to find the value(s) of x.