Question

Evaluate:
$\sqrt{\left(92 + \sqrt{\left(60 + \sqrt{\left(11 + \sqrt{(16 + \sqrt{(81)})}\right)}\right)}\right)}$

• A. 10
• B. 13
• C. 6
• D. 9

Answer 1

Answer:

A. 10

The evaluated value of this nested square root expression is 10.

$\sqrt{92 + \sqrt{60 + \sqrt{11 + \sqrt{16 + \sqrt{81}}}}}$

1. Step 1: Solve the innermost square root $\sqrt{81}$:

   • $\sqrt{81} = 9$

   • The expression becomes: $\sqrt{92 + \sqrt{60 + \sqrt{11 + \sqrt{16 + 9}}}}$

2. Step 2: Add and solve the next square root $\sqrt{16 + 9}$:

   • $\sqrt{25} = 5$

   • The expression becomes: $\sqrt{92 + \sqrt{60 + \sqrt{11 + 5}}}$

3. Step 3: Add and solve the next square root $\sqrt{11 + 5}$:

   • $\sqrt{16} = 4$

   • The expression becomes: $\sqrt{92 + \sqrt{60 + 4}}$

4. Step 4: Add and solve the next square root $\sqrt{60 + 4}$:

   • $\sqrt{64} = 8$

   • The expression becomes: $\sqrt{92 + 8}$

5. Step 5: Solve the final outer square root $\sqrt{92 + 8}$:

   • $\sqrt{100} = \mathbf{10}$