Question

Evaluate:

$\sqrt{\left(42 + \sqrt{\left(40 + \sqrt{\left(74 + \sqrt{(42 + \sqrt{(49)})}\right)}\right)}\right)}$

• A. 7
• B. 9
• C. 5
• D. 6

Answer 1

Answer:

A. 7

The evaluated value of this nested square root expression is 7.

$\sqrt{42 + \sqrt{40 + \sqrt{74 + \sqrt{42 + \sqrt{49}}}}}$

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

* $\sqrt{49} = 7$

* The expression becomes: $\sqrt{42 + \sqrt{40 + \sqrt{74 + \sqrt{42 + 7}}}}$

2. Step 2: Add and solve the next square root $\sqrt{42 + 7}$:

* $\sqrt{49} = 7$

* The expression becomes: $\sqrt{42 + \sqrt{40 + \sqrt{74 + 7}}}$

3. Step 3: Add and solve the next square root $\sqrt{74 + 7}$:

* $\sqrt{81} = 9$

* The expression becomes: $\sqrt{42 + \sqrt{40 + 9}}$

4. Step 4: Add and solve the next square root $\sqrt{40 + 9}$:

* $\sqrt{49} = 7$

* The expression becomes: $\sqrt{42 + 7}$

5. Step 5: Solve the final outer square root $\sqrt{42 + 7}$:

* $\sqrt{49} = \mathbf{7}$