GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If √√√(3x) = 4√(2x), what is the greatest possible value of
[#permalink]
21 Nov 2017, 00:55
21 Nov 2017, 00:55
2
5
Bookmarks
00:00
Question Stats:
75% (01:08) correct
24% (01:39) wrong based on 33 sessions
Hide Show timer Statistics
If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x?
Kudos for correct solution.
Show: :: OA
0.75
Kudos for correct solution.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If \sqrt * \sqrt* \sqrt 3x
[#permalink]
21 Apr 2019, 06:42
21 Apr 2019, 06:42
4
1
Bookmarks
Carcass wrote:
If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\) , what is the greatest possible value of x?
Show: :: OA
0.75
Key concept #1: \(\sqrt{k} = k^{\frac{1}{2}}\)
Key concept #2: \(\sqrt[4]{k} = k^{\frac{1}{4}}\)
So, take: \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\)
Rewrite as: \((((3x)^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}} = (2x)^{\frac{1}{4}}\)
Apply the power of a power law to get: \((3x)^{\frac{1}{8}}=(2x)^{\frac{1}{4}}\)
Raise both sides to the power of 8 to get: \(((3x)^{\frac{1}{8}})^8=((2x)^{\frac{1}{4}})^8\)
Apply the power of a power law to get: \((3x)^1=(2x)^2\)
Simplify to get: \(3x=4x^2\)
Rewrite as: \(4x^2-3x=0\)
Factor: \(x(4x-3)=0\)
So, EITHER \(x = 0\) OR \(4x-3=0\)
If \(4x-3=0\), then \(x=\frac{3}{4}=0.75\)
What is the greatest possible value of x?
Answer: 0.75
RELATED VIDEO
General Discussion
Re: If √√√(3x) = 4√(2x), what is the greatest possible value of
[#permalink]
24 Nov 2017, 22:41
24 Nov 2017, 22:41
2/9 ?
