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# Radical Expressions and Equations

Combine your skills of working with exponents and manipulating expressions for radical glory.

# Infinitely Nested Radicals

What's the correct statement about $$x$$?

$x = \sqrt{x - \sqrt{x - \sqrt{x \ldots } }}$

Hint: The expression marked in purple below is equivalent to $$x$$. Use substitution!

$x = \sqrt{\sqrt{3\sqrt{\sqrt{3\sqrt{\sqrt{3} \ldots}}}}}$

Which of these is a solution for $$x$$?

Hint: The expression marked in purple below is equivalent to $$x$$. Use substitution!

$x = \sqrt{2\sqrt[3]{5\sqrt{2\sqrt[3]{5 \ldots}}}}$

Which of these is a solution for $$x$$?

$x = \sqrt{2 \sqrt{x \sqrt{3 \sqrt{2 \sqrt{x \sqrt{3 \ldots } }}}}}$

What's the nonzero solution for $$x$$?

$x = \sqrt{a \sqrt{a \sqrt{a \sqrt{a \ldots }}}}$

If $$a$$ is nonzero, which of these does $$x$$ equal?

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