Simplify [3]x [3]x [3]x x

Free Practice Question

PS · Problem Solving

605-655

Roots

Simplify $\sqrt[3]{x \sqrt[3]{x \sqrt[3]{x \sqrt{x}}}}$

Correct answer marked below

\sqrt{x}

Correct

\sqrt[3]{x^2}

\sqrt[27]{x^2}

\sqrt[54]{x}

\sqrt[81]{x^{80}}

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Explanation

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Comments

AshutoshSep 8

Nested radicals always trip me up. Do you start from the innermost root and work outward?

AbhigyanSep 13

Yeah, that's what I did. The tricky part is getting the exponents right when you convert each root.

AkshithSep 21

Same here, I always lose track of which exponent goes where.

ColinJun 21

I converted everything to fractional exponents and it made way more sense. The innermost sqrt(x) is x^(1/2), then keep multiplying as you go out.

GunjeetJul 1

Exactly, that's the cleanest way. Just add the exponents carefully!

JwarkJun 7

Wait, option E has 81 and 80 in it, that seems like a trap for people who over-multiply somewhere. This one is tricky for a 605-655.

NicolasJun 19

For sure, I initially got something totally different before I slowed down.

Nabir1d ago

Got it right but took me longer than it should have. Thanks for the clear setup!

What this question tests

Your handling of square and higher roots, including simplifying radicals.

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.