If \(x \geq 0,\) then \(\sqrt{0.49x^{16}}\) must be equal to

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

If \(x \geq 0,\) then \(\sqrt{0.49x^{16}}\) must be equal to

by VJesus12 » Mon May 11, 2020 6:30 am

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If \(x \geq 0,\) then \(\sqrt{0.49x^{16}}\) must be equal to

A. \(0.07x^8\)

B. \(0.07x^4\)

C. \(0.7x^{14}\)

D. \(0.7x^8\)

E. \(0.7x^4\)

[spoiler]OA=D[/spoiler]

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Mon May 11, 2020 6:30 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: If \(x \geq 0,\) then \(\sqrt{0.49x^{16}}\) must be equal to

by Scott@TargetTestPrep » Thu May 21, 2020 5:41 am

VJesus12 wrote: ↑
Mon May 11, 2020 6:30 am
If \(x \geq 0,\) then \(\sqrt{0.49x^{16}}\) must be equal to

A. \(0.07x^8\)

B. \(0.07x^4\)

C. \(0.7x^{14}\)

D. \(0.7x^8\)

E. \(0.7x^4\)

[spoiler]OA=D[/spoiler]

Solution:

√(0.49x^16) = √0.49 * √(x^16) = 0.7 * x^8 = 0.7x^8

(Note: Technically, √(x^16) = |x^8|. However, |x^8| = x^8 regardless x is positive or negative or zero. That is, the answer would be the same even if “x ≥ 0” is not mentioned in the problem.)

Answer: D

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