Question

Evaluate:

$\sqrt{\left(3 + \sqrt{\left(32 + \sqrt{\left(8 + \sqrt{(57 + \sqrt{(49)})}\right)}\right)}\right)}$

• A. 3
• B. 5
• C. 6
• D. 4

Answer 1

Answer:

A. 3

The evaluated value of the nested square root expression is 3.

$\sqrt{3 + \sqrt{32 + \sqrt{8 + \sqrt{57 + \sqrt{49}}}}}$

1. Step 1: Solve the innermost square root $\sqrt{49}$:

* $\sqrt{49} = 7$

* The expression becomes: $\sqrt{3 + \sqrt{32 + \sqrt{8 + \sqrt{57 + 7}}}}$

2. Step 2: Add and solve the next square root $\sqrt{57 + 7}$:

* $\sqrt{64} = 8$

* The expression becomes: $\sqrt{3 + \sqrt{32 + \sqrt{8 + 8}}}$

3. Step 3: Add and solve the next square root $\sqrt{8 + 8}$:

* $\sqrt{16} = 4$

* The expression becomes: $\sqrt{3 + \sqrt{32 + 4}}$

4. Step 4: Add and solve the next square root $\sqrt{32 + 4}$:

* $\sqrt{36} = 6$

* The expression becomes: $\sqrt{3 + 6}$

5. Step 5: Solve the final outer square root $\sqrt{3 + 6}$:

* $\sqrt{9} = \mathbf{3}$