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Of the following, which is greatest?

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by Jay@ManhattanReview » Mon Dec 30, 2019 9:30 pm
BTGmoderatorDC wrote:Of the following, which is greatest?

A. \(3\sqrt{2}\)

B. \(2\sqrt{3}\)

C. \(\frac{4\sqrt{3}}{5}\)

D. \(\frac{5\sqrt{2}}{4}\)

C. \(\frac{7}{\sqrt{3}}\)

OA A

Source: Official Guide
Since numbers in all options are in square roots, let's square them and compare.

A. \(3\sqrt{2}\): Square of \(3\sqrt{2}\) = 18

B. \(2\sqrt{3}\): Square of \(2\sqrt{3}\) = 12 < 18, Option A

C. \(\frac{4\sqrt{3}}{5}\): Square of \(\frac{4\sqrt{3}}{5}\) = 16*3/25 = 48/25 < 18, Option A

D. \(\frac{5\sqrt{2}}{4}\): Square of \(\frac{5\sqrt{2}}{4}\) = 25/8 < 18, Option A

C. \(\frac{7}{\sqrt{3}}\): Square of \(\frac{7}{\sqrt{3}}\) = 49/3 = 16.33 < 18, Option A

The correct answer: A

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Sun Jan 05, 2020 8:03 pm
BTGmoderatorDC wrote:Of the following, which is greatest?

A. \(3\sqrt{2}\)

B. \(2\sqrt{3}\)

C. \(\frac{4\sqrt{3}}{5}\)

D. \(\frac{5\sqrt{2}}{4}\)

C. \(\frac{7}{\sqrt{3}}\)

OA A

Source: Official Guide
Since all the numbers are positive, we can square them (to remove the square root), and the one with the largest square is the one that has the greatest value. The following are the squares of the numbers.

A. 9 x 2 = 18

B. 4 x 3 = 12

C. 16 x 3 / 25 = 48/25 < 2

D. 25 x 2 / 16 = 50/16 < 4

E. 49/3 < 17

We see that 3√2 is the greatest since its square is the greatest.

Answer: A

Scott Woodbury-Stewart
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