1970 AHSME Problems/Problem 1

Problem

The fourth power of $\sqrt{1+\sqrt{1+\sqrt{1}}}$ is

$\text{(A) } \sqrt{2}+\sqrt{3}\quad \text{(B) } \tfrac{1}{2}(7+3\sqrt{5})\quad \text{(C) } 1+2\sqrt{3}\quad \text{(D) } 3\quad \text{(E) } 3+2\sqrt{2}$

Solution

We can simplify the expression to $\sqrt{1+\sqrt{2}}$ Then we square it so it is now $1+\sqrt{2}$ . We still have to square it one more time, getting $\boxed{(E)\ 3+2\sqrt{2}}$ .

1970 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 2
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1970 AHSME Problems/Problem 1

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