Algebra
# Algebraic Manipulation

Express \(y\) in terms of \(x\).

\[\Large\sqrt[3]{3\sqrt[3]{3\sqrt[3]{3\cdots}}}=\sqrt{n} \quad, \quad n = \ ? \]

\(x=\sqrt { 2+\sqrt { 2+\sqrt { 2+\sqrt { 2\ldots } } } } \)

What is the value of \(x\)?

\[ \huge{ x^{x^{x^{x^{x^{.^{.^.}}}}}}=2} \]

Find the value of \(x\) that satisfies the equation above.

\[ \large \sqrt{12+\sqrt{12+\sqrt{12+\sqrt{12 + ...}}}}= \ ? \]

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