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sqrt of 3 or sqrt(3) of 9
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31 Dec 2021, 07:33
31 Dec 2021, 07:33
2
Expert Reply
00:00
Question Stats:
66% (00:36) correct
33% (00:39) wrong based on 48 sessions
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Quantity A |
Quantity B |
\((\sqrt{3})^{20}\) |
\((\sqrt[3]{9})^{15}\) |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
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Re: sqrt of 3 or sqrt(3) of 9
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31 Dec 2021, 07:41
31 Dec 2021, 07:41
3
Carcass wrote:
Quantity A |
Quantity B |
\((\sqrt{3})^{20}\) |
\((\sqrt[3]{9})^{15}\) |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Key property #1: \(\sqrt{x} = x^{\frac{1}{2}}\)
Key property #2: \(\sqrt[3]{x}= x^{\frac{1}{3}}\)
We can now rewrite the quantities as follows:
QUANTITY A: \((3^{\frac{1}{2}})^{20}\)
QUANTITY B: \((9^{\frac{1}{3}})^{15}\)
Apply the Power of a Power law to get:
QUANTITY A: \(3^{10}\)
QUANTITY B: \(9^{5}\)
Rewrite \(9\) as \(3^2\) to get:
QUANTITY A: \(3^{10}\)
QUANTITY B: \((3^2)^{5}\)
Apply the Power of a Power law to Quantity B to get:
QUANTITY A: \(3^{10}\)
QUANTITY B: \(3^{10}\)
Answer: C
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Re: sqrt of 3 or sqrt(3) of 9
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30 May 2023, 23:05
30 May 2023, 23:05
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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