Question

If \( \sqrt{x} + 14 = \sqrt{2601} \), then \( x \) is equal to:

• A. 1359
• B. 1379
• C. 1369
• D. 1309

Hint:

When solving equations with square roots, isolate the square root term first, then square both sides to eliminate the root.

Answer 1

The Correct Option is C

Step 1: Simplify the right-hand side. We are given: \[ \sqrt{x} + 14 = \sqrt{2601} \] Now, simplify \( \sqrt{2601} \): \[ \sqrt{2601} = 51 \] Step 2: Solve for \( \sqrt{x} \). \[ \sqrt{x} + 14 = 51 \quad \Rightarrow \quad \sqrt{x} = 51 - 14 = 37 \] Step 3: Square both sides to find \( x \). \[ x = 37^2 = 1369 \]