Question

If \[ \sqrt{218 + \sqrt{37 + \sqrt{144}}} = K, \text{ then value of } K \text{ is} \]

• A. 35
• B. 25
• C. 20
• D. 15

Hint:

Always evaluate nested square roots from the innermost to the outermost. Simplify step-by-step to avoid errors.

Answer 1

The Correct Option is C

We will simplify the expression step by step, starting from the innermost square root. Step 1: Simplify the Innermost Square Root \[ \sqrt{144} = 12 \quad \text{(since } 12 \times 12 = 144\text{)} \] Step 2: Substitute and Simplify the Next Level \[ \sqrt{37 + \sqrt{144}} = \sqrt{37 + 12} = \sqrt{49} = 7 \quad \text{(since } 7 \times 7 = 49\text{)} \] Step 3: Simplify the Outermost Expression \[ \sqrt{218 + \sqrt{37 + \sqrt{144}}} = \sqrt{218 + 7} = \sqrt{225} = 15 \quad \text{(since } 15 \times 15 = 225\text{)} \] Verification Let's verify each step: \begin{itemize} \item \(\sqrt{144} = 12\) is correct as \(12^2 = 144\) \item \(37 + 12 = 49\) and \(\sqrt{49} = 7\) are correct \item \(218 + 7 = 225\) and \(\sqrt{225} = 15\) are correct \end{itemize} Final Answer After simplifying all nested square roots, we find: \[ K = \boxed{15} \]