Question

If \( \sqrt{x + 9} = 5 \), then the value of \( x \) is:

• A. 14
• B. 15
• C. 16
• D. 25

Hint:

For simple algebraic equations, you can use the substitution method to test options directly! Try option (a): $\sqrt{14+9} = \sqrt{23} \neq 5$ Try option (c): $\sqrt{16+9} = \sqrt{25} = 5$. Since 16 is the only number that produces a perfect square of 25 under the root, it must be the correct answer!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question presents a basic radical (square root) equation. To solve an algebraic equation where the variable is locked inside a principal square root, the primary objective is to eliminate the radical sign. This is achieved by applying the exact inverse operation of a square root, which is squaring both sides of the equation.

Step 2: Key Formula or Approach:
The squaring property of equality states that if two expressions are equal ($a = b$), then their squares are also equal ($a^2 = b^2$). For any valid radical expression, squaring removes the root: $$\left(\sqrt{f(x)}\right)^2 = f(x)$$

Step 3: Detailed Explanation:
Let's look at the given equation: $$\sqrt{x + 9} = 5$$ Apply the squaring property to both sides of the equation to clear the radical: $$\left(\sqrt{x + 9}\right)^2 = (5)^2$$ $$x + 9 = 25$$ Now, isolate the variable $x$ by performing subtraction (subtracting 9 from both sides): $$x = 25 - 9$$ $$x = 16$$ We can easily verify our result by substituting $x = 16$ back into the original expression: $$\text{LHS} = \sqrt{16 + 9} = \sqrt{25} = 5 = \text{RHS}$$ Since both sides match perfectly, the value is verified.

Step 4: Final Answer:
The value of $x$ is 16.