CPM Homework Help : APCALC Problem 10-108

Review Ying’s technique for manipulating infinite expressions in problem 9-45. Then, use this strategy to evaluate the infinite “nested radical” $\sqrt { 3 + \sqrt { 3 + \sqrt { 3 + \ldots } } }$

Step 1:

$\text{Let }S=\sqrt{3+\sqrt{3+...}}$

Step 2:

$S=\sqrt{3+S}$

Step 3:

$S^2=3+S$

Now solve for $S$ using the Quadratic Formula.