Which of the following statements is true? | GMAT Sprint

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PS · Problem Solving

705-805

Roots

Which of the following statements is true?

Correct answer marked below

3\sqrt{7}<2\sqrt{15}<\frac{5\sqrt{13}}{\sqrt{5}}<\frac{39}{5}

2\sqrt{15}<\frac{39}{5}<3\sqrt{7}<\frac{5\sqrt{13}}{\sqrt{5}}

Correct

2\sqrt{15}<3\sqrt{7}<\frac{39}{5}<\frac{5\sqrt{13}}{\sqrt{5}}

2\sqrt{15}<3\sqrt{7}<\frac{5\sqrt{13}}{\sqrt{5}}<\frac{39}{5}

2\sqrt{15}<\frac{5\sqrt{13}}{\sqrt{5}}<3\sqrt{7}<\frac{39}{5}

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Explanation

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Official Explanation

Official

Convert all numbers to square roots:

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3\sqrt{7}

\sqrt{63}

2\sqrt{15}

\sqrt{60}

\frac{5\sqrt{13}}{\sqrt{5}}

\sqrt{65}

\frac{39}{5}

\sqrt{(7.8)^2}

\sqrt{60.84}

…

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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.