Which of the numbers -3 73, -7 97, - 37 21, - 13 63, and -9 13 is the greatest?

Which of the numbers -3 73, -7 97, - 37 21, -… | GMAT Sprint

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PS · Problem Solving

705-805

Roots

Which of the numbers $-3\sqrt{\frac{7}{3}}$ , $-7\sqrt{\frac{9}{7}}$ , $-\frac{3}{7}\sqrt{21}$ , $-\frac{1}{3}\sqrt{63}$ , and $-9\sqrt{\frac{1}{3}}$ is the greatest?

Correct answer marked below

-3\sqrt{\frac{7}{3}}

-7\sqrt{\frac{9}{7}}

-\frac{3}{7}\sqrt{21}

Correct

-\frac{1}{3}\sqrt{63}

-9\sqrt{\frac{1}{3}}

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Explanation

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Square all of them (since all are negative, the smallest squared value corresponds to the greatest original number).

Squared values:

A:

\left(-3\sqrt{\frac{7}{3}}\right)^2 = 9 \cdot \frac{7}{3} = 21

\left(-7\sqrt{\frac{9}{7}}\right)^2 = 49 \cdot \frac{9}{7} = 63

\left(-\frac{3}{7}\sqrt{21}\right)^2 = \frac{9}{49} \cdot 21 = \frac{189}{49} = \frac{27}{7} \approx 3.857

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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.