Which of the following is ranked in increasin… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Roots

Which of the following is ranked in increasing order from left to right?

Correct answer marked below

\sqrt[4]{2}

\sqrt[9]{6}

\sqrt[36]{1290}

\sqrt[18]{35}

\sqrt[4]{2}

\sqrt[18]{35}

\sqrt[36]{1290}

\sqrt[9]{6}

Correct

\sqrt[9]{6}

\sqrt[4]{2}

\sqrt[18]{35}

\sqrt[36]{1290}

\sqrt[4]{2}

\sqrt[36]{1290}

\sqrt[9]{6}

\sqrt[18]{35}

\sqrt[18]{35}

\sqrt[4]{2}

\sqrt[9]{6}

\sqrt[36]{1290}

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Explanation

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Official Explanation

Official

We have four terms:

\sqrt[4]{2}

\sqrt[9]{6}

\sqrt[36]{1290}

\sqrt[18]{35}

. The roots are 4th, 9th, 18th and 36th, so let us raise each to the power equal to LCM(4,9,18,36) or 36.

(\sqrt[4]{2})^{36}=2^9=512

(\sqrt[9]{6})^{36}=6^4=1296

…

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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.