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Difficulty:
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Question Stats:
80% (01:17) correct
20%
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Which of the numbers \(\frac{\sqrt{5}}{2}\), \(\sqrt{\frac{5}{2} }\), \(\frac{2}{\sqrt{5}}\) \(\sqrt{\frac{2}{5} }\), and \(\frac{1}{\sqrt{5}}\) is the greatest?
A. \(\frac{\sqrt{5}}{2}\),
B. \(\sqrt{\frac{5}{2} }\)
C. \(\frac{2}{\sqrt{5}}\)
D. \(\sqrt{\frac{2}{5} }\)
E. \(\frac{1}{\sqrt{5}}\)
A. \(\frac{\sqrt{5}}{2}\),
B. \(\sqrt{\frac{5}{2} }\)
C. \(\frac{2}{\sqrt{5}}\)
D. \(\sqrt{\frac{2}{5} }\)
E. \(\frac{1}{\sqrt{5}}\)
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13 Aug 2023, 15:17
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Bunuel
The square of positive numbers will always have the same ascending order as that of the original numbers.
(√5/2)^2 = 5/4
[√(5/2)]^2 = 5/2
(2/√5)^2 = 4/5
[√(2/5)]^2 = 2/5
(1/√5)^2 = 1/5
Since 5/2 is the greatest among the values of the squared expressions, the greatest among the original numbers must be √(5/2).
Answer: B
13 Aug 2023, 14:09
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Which of the numbers \(\frac{\sqrt{5}}{2}\), \(\sqrt{\frac{5}{2} }\), \(\frac{2}{\sqrt{5}}\) \(\sqrt{\frac{2}{5} }\), and \(\frac{1}{\sqrt{5}}\) is the greatest?
A. \(\frac{\sqrt{5}}{2}\)
B. \(\sqrt{\frac{5}{2} }\)
C. \(\frac{2}{\sqrt{5}}\)
D. \(\sqrt{\frac{2}{5} }\)
E. \(\frac{1}{\sqrt{5}}\)
Since \(\sqrt{4}= 2\), we know that \(\sqrt{5} > 2\).
Thus, any of the choices in which \(\sqrt{5}\) is over 2 must be greater than any of the choices in which \(\sqrt{5}\) or 5 is under 2, or 1.
So, we can eliminate (C), (D), and (E), and we have to decide between (A) and (B), in other words, between \(\frac{\sqrt{5}}{2}\) and \(\sqrt{\frac{5}{2} }\).
To compare (A) and (B), notice that \(\sqrt{\frac{5}{2} } = \frac{\sqrt{5}}{\sqrt{2}}\).
Thus, since \(\sqrt{2} < 2\), we know that choice (A) \(\frac{\sqrt{5}}{2}\) is less than \(\frac{\sqrt{5}}{\sqrt{2}}\), which is equal to choice (B).
Thus. the correct answer is (B).
A. \(\frac{\sqrt{5}}{2}\)
B. \(\sqrt{\frac{5}{2} }\)
C. \(\frac{2}{\sqrt{5}}\)
D. \(\sqrt{\frac{2}{5} }\)
E. \(\frac{1}{\sqrt{5}}\)
Since \(\sqrt{4}= 2\), we know that \(\sqrt{5} > 2\).
Thus, any of the choices in which \(\sqrt{5}\) is over 2 must be greater than any of the choices in which \(\sqrt{5}\) or 5 is under 2, or 1.
So, we can eliminate (C), (D), and (E), and we have to decide between (A) and (B), in other words, between \(\frac{\sqrt{5}}{2}\) and \(\sqrt{\frac{5}{2} }\).
To compare (A) and (B), notice that \(\sqrt{\frac{5}{2} } = \frac{\sqrt{5}}{\sqrt{2}}\).
Thus, since \(\sqrt{2} < 2\), we know that choice (A) \(\frac{\sqrt{5}}{2}\) is less than \(\frac{\sqrt{5}}{\sqrt{2}}\), which is equal to choice (B).
Thus. the correct answer is (B).
