Simplify √(5 + √11) - Nested Radical Problem

The problem asks us to simplify .

This is a nested radical, where we have a square root inside another square root.

To simplify this, we can use the following method:
Let

Square both sides:

Subtract 5 from both sides:

Square both sides again:

Expand:

Rearrange:

This is a quadratic equation in . Let :

We can solve this using the quadratic formula:

Here, , , and

Plugging into the formula:

Since we’re looking for a positive solution (as is a square root), we take the positive root:

Remember, , so: