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555-605 (Medium)|   Algebra|   Roots|      
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Bunuel
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If √√√(3x) = 4√(2x), what is the greatest possible value of x? 07 Dec 2018, 02:35
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C
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35% (medium)

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74% (01:48) correct 26% (02:12) wrong based on 600 sessions

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If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x?

A. 1/4
B. 1/2
C. 3/4
D. 4/3
E. 8/3
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C
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If √√√(3x) = 4√(2x), what is the greatest possible value of x? 07 Dec 2018, 02:44
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(3x)^(1/8) = (2x)^(1/4)

Taking 8th power on both sides.

3x = 4x^2
4x^2-3x = 0.
x(4x-3) = 0.
x = 0 or 3/4.

C is the answer

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If √√√(3x) = 4√(2x), what is the greatest possible value of x? 07 Dec 2018, 02:51
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If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x?

A. 1/4
B. 1/2
C. 3/4
D. 4/3
E. 8/3
Show more


we can solve by plugin values as well:

upon doing plugin at x=3/4
we would get value
(3/2)^1/4 = (3/2)^1/4

IMO C , x=3/4 is correct.
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If √√√(3x) = 4√(2x), what is the greatest possible value of x? 07 Dec 2018, 03:03
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Bunuel
If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x?

A. 1/4
B. 1/2
C. 3/4
D. 4/3
E. 8/3




we can solve by plugin values as well:

upon doing plugin at x=3/4
we would get value
(3/2)^1/4 = (3/2)^1/4

IMO C , x=3/4 is correct.
Show more

Archit3110, how did you choose 3/4 to plugin?

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If √√√(3x) = 4√(2x), what is the greatest possible value of x? 07 Dec 2018, 03:08
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Afc0892
Archit3110
Bunuel
If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x?

A. 1/4
B. 1/2
C. 3/4
D. 4/3
E. 8/3




we can solve by plugin values as well:

upon doing plugin at x=3/4
we would get value
(3/2)^1/4 = (3/2)^1/4

IMO C , x=3/4 is correct.

Archit3110, how did you choose 3/4 to plugin?

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Afc0892
I plugged in from the given value of x into the question
Given LHS
(3*x)^1/8
so upon plugin it becomes
(9/4)^1/8 or we can say ( 3/2)^1/4

and RHS given (2x)^1/4 upon plug in x=3/4 we would get , ( 3/2)^1/4

hence LHS = RHS so sufficient..
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If √√√(3x) = 4√(2x), what is the greatest possible value of x? 07 Dec 2018, 03:42
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Bunuel
If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\), what is the greatest possible value of x?

A. 1/4
B. 1/2
C. 3/4
D. 4/3
E. 8/3
Show more

Ans. √√√(3x) = (3x)^(1/2*1/2*1/2)=(3x)^1/8
(3x)^1/8=(2x)^1/4
3x=(2x)^2
4x^2-3x=0
x(4x-3)=0
x=0 or x=3/4
Ans.C
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If √√√(3x) = 4√(2x), what is the greatest possible value of x? 12 Jan 2019, 17:19
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Afc0892
(3x)^(1/8) = (2x)^(1/4)

Taking 8th power on both sides.

3x = 4x^2
4x^2-3x = 0.
x(4x-3) = 0.
x = 0 or 3/4.

C is the answer

Posted from my mobile device
Show more

Hello Afc0892 !

Could you please give a detailed explanation on how to get rid of the square roots?

Kind regards!
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If √√√(3x) = 4√(2x), what is the greatest possible value of x? 15 Jan 2019, 22:28
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jfranciscocuencag
Afc0892
(3x)^(1/8) = (2x)^(1/4)

Taking 8th power on both sides.

3x = 4x^2
4x^2-3x = 0.
x(4x-3) = 0.
x = 0 or 3/4.

C is the answer

Posted from my mobile device

Hello Afc0892 !

Could you please give a detailed explanation on how to get rid of the square roots?

Kind regards!
Show more

Hey jfranciscocuencag, Sure. :)

\(\sqrt{}\) can be written as any number power \(\frac{1}{2}\)
As the question contains 3 squareroots. 3x will have a power of \(\frac{1}{8} (\frac{1}{2}*\frac{1}{2}*\frac{1}{2})\)
And 2x has fourth power root. hence \((2x)^\frac{1}{4}\)

In order to cancel the root power, we'll take 8th power on both sides (as LCM of 4 and 8 is 8).
Then the equation can be written as 3x = \((2x)^2\)
Reducing this further will yield x as 0 or 3/4.

Hope it's clear.
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If √√√(3x) = 4√(2x), what is the greatest possible value of x? Updated on: 20 Oct 2022, 05:18
Originally posted by KarishmaB on 16 Jan 2019, 03:40.
Last edited by KarishmaB on 20 Oct 2022, 05:18, edited 1 time in total.
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jfranciscocuencag
Afc0892
(3x)^(1/8) = (2x)^(1/4)

Taking 8th power on both sides.

3x = 4x^2
4x^2-3x = 0.
x(4x-3) = 0.
x = 0 or 3/4.

C is the answer

Posted from my mobile device

Hello Afc0892 !

Could you please give a detailed explanation on how to get rid of the square roots?

Kind regards!
Show more

Check out the blog posts on the link given in my signature.
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If √√√(3x) = 4√(2x), what is the greatest possible value of x? 16 Jan 2019, 15:31
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jfranciscocuencag
Afc0892
(3x)^(1/8) = (2x)^(1/4)

Taking 8th power on both sides.

3x = 4x^2
4x^2-3x = 0.
x(4x-3) = 0.
x = 0 or 3/4.

C is the answer

Posted from my mobile device

Hello Afc0892 !

Could you please give a detailed explanation on how to get rid of the square roots?

Kind regards!

Hey jfranciscocuencag, Sure. :)

\(\sqrt{}\) can be written as any number power \(\frac{1}{2}\)
As the question contains 3 squareroots. 3x will have a power of \(\frac{1}{8} (\frac{1}{2}*\frac{1}{2}*\frac{1}{2})\)
And 2x has fourth power root. hence \((2x)^\frac{1}{4}\)

In order to cancel the root power, we'll take 8th power on both sides (as LCM of 4 and 8 is 8).
Then the equation can be written as 3x = \((2x)^2\)
Reducing this further will yield x as 0 or 3/4.

Hope it's clear.
Show more

Thank you Afc0892 !

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If √√√(3x) = 4√(2x), what is the greatest possible value of x? 16 Aug 2025, 03:46
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