This is the exciting part of quadratic equations. It is fun to see dancing radicals like this . This is an unending chain of radical expression and can be surprisingly simplified using quadratic equations.

**Worked Problem 1:**

can be simplified in the form of . Find the value of

Let

By squaring both sides;

Since , by substitution

or

Since we are looking for x we can use quadratic formula to solve for it.

Only keep the positive x.

Therefore,

**Worked Problem 2:**

Simplify the radical .

Let

By squaring both sides

Since by substitution

or

By factoring

and

**Worked Problem 3:**

Find x if . What is the value of x?

Since by substitution