Question

Simplify \(\sqrt{54-\sqrt{20+\sqrt{32-\sqrt{49}}}}\)

• A. \(\sqrt{17}\)
• B. 7
• C. 17
• D. \(3\sqrt{17}\)

Answer 1

The Correct Option is B

To simplify \(\sqrt{54-\sqrt{20+\sqrt{32-\sqrt{49}}}}\), we follow these steps:

Step 1: Simplify the innermost expression, \(\sqrt{49}\). Since \(49=7^2\), we have \(\sqrt{49}=7\).

Step 2: Substitute back into the expression: \(\sqrt{32-\sqrt{49}} = \sqrt{32-7} = \sqrt{25}\). Knowing \(25=5^2\), we simplify to \(\sqrt{25}=5\).

Step 3: Substitute again: \(\sqrt{20+\sqrt{32-\sqrt{49}}} = \sqrt{20 + 5} = \sqrt{25}\), and \(\sqrt{25}=5\).

Step 4: Finally, substitute one last time: \(\sqrt{54-\sqrt{20+\sqrt{32-\sqrt{49}}}} = \sqrt{54-5} = \sqrt{49}\), and so \(\sqrt{49}=7\).

Therefore, the simplified value is \(7\).