Which of the following values is greater than 2? i. [3]3 ii. [4]4 iii. [5]5

Which of the following values is greater than… | GMAT Sprint

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PS · Problem Solving

705-805

Roots

Which of the following values is greater than $\sqrt{2}$ ?
i. $\sqrt[3]{3}$
ii. $\sqrt[4]{4}$
iii. $\sqrt[5]{5}$

Correct answer marked below

i only

Correct

ii only

iii only

i and iii

i, ii and iii

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Explanation

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\sqrt{2}=2^{\frac{1}{2}}=2^{\frac{3}{6}}=8^{\frac{1}{6}}

And,

\sqrt{2}=2^{\frac{1}{2}}=2^{\frac{2}{4}}=4^{\frac{1}{4}}

And,

\sqrt{2}=2^{\frac{1}{2}}=2^{\frac{5}{10}}=32^{\frac{1}{10}}

\sqrt[3]{3}=3^{\frac{1}{3}}=3^{\frac{2}{6}}=9^{\frac{1}{6}}

…

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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.