Question

Evaluate:
$\sqrt{\left(76 + \sqrt{\left(21 + \sqrt{\left(9 + \sqrt{(40 + \sqrt{(81)})}\right)}\right)}\right)}$

• A. 9
• B. 11
• C. 12
• D. 8

Answer 1

Answer:

A. 9

The evaluated value of this nested square root expression is 9.

$\sqrt{76 + \sqrt{21 + \sqrt{9 + \sqrt{40 + \sqrt{81}}}}}$

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

* $\sqrt{81} = 9$

* The expression becomes: $\sqrt{76 + \sqrt{21 + \sqrt{9 + \sqrt{40 + 9}}}}$

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

* $\sqrt{49} = 7$

* The expression becomes: $\sqrt{76 + \sqrt{21 + \sqrt{9 + 7}}}$

3. Step 3: Add and solve the next square root $\sqrt{9 + 7}$:

* $\sqrt{16} = 4$

* The expression becomes: $\sqrt{76 + \sqrt{21 + 4}}$

4. Step 4: Add and solve the next square root $\sqrt{21 + 4}$:

* $\sqrt{25} = 5$

* The expression becomes: $\sqrt{76 + 5}$

5. Step 5: Solve the final outer square root $\sqrt{76 + 5}$:

* $\sqrt{81} = \mathbf{9}$