Question

Evaluate:

$\sqrt{\left(20 + \sqrt{\left(22 + \sqrt{\left(2 + \sqrt{(40 + \sqrt{(81)})}\right)}\right)}\right)}$

• A. 9
• B. 7
• C. 5
• D. 6

Answer 1

Answer:

C. 5

The evaluated value of this nested square root expression is 5.

$\sqrt{20 + \sqrt{22 + \sqrt{2 + \sqrt{40 + \sqrt{81}}}}}$

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

   • $\sqrt{81} = 9$

   • The expression becomes: $\sqrt{20 + \sqrt{22 + \sqrt{2 + \sqrt{40 + 9}}}}$

2. Step 2: Add and solve the next square root $\sqrt{40 + 9}$:

   • $\sqrt{49} = 7$

   • The expression becomes: $\sqrt{20 + \sqrt{22 + \sqrt{2 + 7}}}$

3. Step 3: Add and solve the next square root $\sqrt{2 + 7}$:

   • $\sqrt{9} = 3$

   • The expression becomes: $\sqrt{20 + \sqrt{22 + 3}}$

4. Step 4: Add and solve the next square root $\sqrt{22 + 3}$:

   • $\sqrt{25} = 5$

   • The expression becomes: $\sqrt{20 + 5}$

5. Step 5: Solve the final outer square root $\sqrt{20 + 5}$:

   • $\sqrt{25} = \mathbf{5}$