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NEW!!! Tough and tricky exponents and roots questions

brainwired

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Joined: 18 May 2023

Posts: 28

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Concentration: General Management, Leadership

GMAT 1: 600 Q48 V25 Verified score

Re: NEW!!! Tough and tricky exponents and roots questions [#permalink]

23 Jul 2023, 22:31

Bunuel said any positive int root from a number more than one is more than one.

\(\sqrt[1000]{2}\)>1 but that means it is 2^(1/1000) right? How is that greater than 1?

Bunuel

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Joined: 02 Sep 2009

Posts: 90078

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Re: NEW!!! Tough and tricky exponents and roots questions [#permalink]

23 Jul 2023, 23:46

1

Kudos

Expert Reply

brainwired wrote:

Bunuel said any positive int root from a number more than one is more than one.

\(\sqrt[1000]{2}\)>1 but that means it is 2^(1/1000) right? How is that greater than 1?

\(\sqrt[1000]{2} \approx 1.000693...\)

Also, consider this: let \(\sqrt[1000]{2} = x\), where x > 0. Then \(2 = x^{1000}\). Now, if x were less than 1, then \(x^{1000}\) would be less than x (when taking a number between 0 and 1 to a positive integer power, its value decreases. For instance, (1/2)^2 = 1/4, which is less than 1/2). Hence, x must be greater than 1.

Hope it's clear.
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Re: NEW!!! Tough and tricky exponents and roots questions [#permalink]

23 Jul 2023, 23:46

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