. If x is a positive number and 1/2 the square root of x is the cube : Problem Solving (PS)

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Bunuel

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. If x is a positive number and 1/2 the square root of x is the cube [#permalink]

25 Aug 2016, 01:25

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A

B

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78% (01:27) correct

22% (01:29) wrong

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If x is a positive number and 1/2 the square root of x is the cube root of x, then x =

A. 64
B. 32
C. 16
D. 4
E. 1

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msk0657

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Re: . If x is a positive number and 1/2 the square root of x is the cube [#permalink]

25 Aug 2016, 05:37

3

Kudos

Bunuel wrote:

If x is a positive number and 1/2 the square root of x is the cube root of x, then x =

A. 64
B. 32
C. 16
D. 4
E. 1

1/2 the square root of x is cube root of x.

if x = 64..

then 1/2 the square root of x = 4 and cube of x is 64.

Option A.

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cptholt

Intern

Joined: 01 Jan 2016

Posts: 28

Location: India

Re: . If x is a positive number and 1/2 the square root of x is the cube [#permalink]

03 Mar 2019, 18:59

1

Kudos

freedomfox2121 wrote:

Hello,

Could someone please explain how to solve this algebraically?

Thanks in advance.

(x)^1/2 / 2 = (x) ^ 3

(x) ^ 1/2 / (x)^3 = 2

(x) ^ 1/6 = 2

x = 64

B

freedomfox2121

Intern

Joined: 21 Jan 2019

Posts: 3

Re: . If x is a positive number and 1/2 the square root of x is the cube [#permalink]

03 Mar 2019, 17:14

Hello,

Could someone please explain how to solve this algebraically?

Thanks in advance.

B

freedomfox2121

Intern

Joined: 21 Jan 2019

Posts: 3

. If x is a positive number and 1/2 the square root of x is the cube [#permalink]

05 Mar 2019, 20:27

jake092 wrote:

freedomfox2121 wrote:

Hello,

Could someone please explain how to solve this algebraically?

Thanks in advance.

(x)^1/2 / 2 = (x) ^ 3

(x) ^ 1/2 / (x)^3 = 2

(x) ^ 1/6 = 2

x = 64

I set up the problem as (x)^1/2 / 2 = (x)^1/3
Is X^1/3 the correct way to write a cube root? My understanding is that x^3 is x cubed.

B

yvankd

Intern

Joined: 18 Feb 2019

Posts: 12

Re: . If x is a positive number and 1/2 the square root of x is the cube [#permalink]

06 Mar 2019, 20:45

freedomfox2121 wrote:

jake092 wrote:

freedomfox2121 wrote:

Hello,

Could someone please explain how to solve this algebraically?

Thanks in advance.

(x)^1/2 / 2 = (x) ^ 3

(x) ^ 1/2 / (x)^3 = 2

(x) ^ 1/6 = 2

x = 64

I set up the problem as (x)^1/2 / 2 = (x)^1/3
Is X^1/3 the correct way to write a cube root? My understanding is that x^3 is x cubed.

I set up the formula as (x)^1/2 / 2 = (x)^1/3
Then simplified to (x)^1/2 = 2(x)^1/3 -> [(x)^1/2] / [(x)^1/3] = 2
Which then turns into (x)^1/6 = 2
6√(x) = 2
Finally, [6√(x)]^6 = (2)^6
x = 64

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shashankism

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Re: . If x is a positive number and 1/2 the square root of x is the cube [#permalink]

29 May 2019, 08:23

Bunuel wrote:

If x is a positive number and 1/2 the square root of x is the cube root of x, then x =

A. 64
B. 32
C. 16
D. 4
E. 1

x>0
1/2 (x^1/2) = x^1/3
square and cube both side. Or take power of 6 on both side.
1/2^6 *x^3 = x^2
x^3 = 2^6 * x^2
x^2(x-2^6) = 0
since x =/=0
Hence x = 2^6 = 64

Answer A

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ScottTargetTestPrep

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Affiliations: Target Test Prep

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Re: . If x is a positive number and 1/2 the square root of x is the cube [#permalink]

01 Jun 2019, 06:18

2

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Expert Reply

Bunuel wrote:

If x is a positive number and 1/2 the square root of x is the cube root of x, then x =

A. 64
B. 32
C. 16
D. 4
E. 1

We can create the equation:

(1/2)√x = ^3√x

(½)x^(½) = x^(⅓)

We can raise each side to the 6th power, obtaining:

[(½)^6](x^3) = x^2

Dividing each side by x^2 (which is possible because x is positive), we have:

(1/64)x = 1

x = 64

Answer: A
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BlueRocketAsh

Manager

Joined: 11 Oct 2019

Posts: 77

. If x is a positive number and 1/2 the square root of x is the cube [#permalink]

03 Jul 2020, 12:18

\(x^1^/^3=\frac{1}{2}\sqrt{x}\)
\(x^2=\frac{1}{64}x^3\)
\(x=64\)

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ScottTargetTestPrep

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Posts: 18730

Location: United States (CA)

Re: . If x is a positive number and 1/2 the square root of x is the cube [#permalink]

05 Jul 2020, 15:06

Expert Reply

Bunuel wrote:

If x is a positive number and 1/2 the square root of x is the cube root of x, then x =

A. 64
B. 32
C. 16
D. 4
E. 1

Solution:

We can create the equation:

½ √x = 3^√x

√x = 2 * 3^√x

Raising each side of the equation to the 6th power, we have:

x^3 = 64x^2

Dividing both sides by x^2 (since x is nonzero), we have:

x = 64

Answer: A
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philipssonicare

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Joined: 15 Feb 2018

Posts: 424

Re: . If x is a positive number and 1/2 the square root of x is the cube [#permalink]

11 Mar 2021, 19:00

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\(\frac{√x}{2}=\sqrt[3]{x}\)

\(\frac{x^{1/2}}{2}=x^{1/3}\)

\(\frac{x^{1/2}}{x^{1/3}}=2\)

\(x^{1/2-1/3}=2\)

\(x^{3/6-2/6}=2\)

\(x^{1/6}=2\)

\(x^{6(1/6)}=2^6\)

\(x^1=64\)

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RiyadhArifin237

Intern

Joined: 04 Nov 2021

Posts: 14

Re: . If x is a positive number and 1/2 the square root of x is the cube [#permalink]

16 May 2022, 13:16

ScottTargetTestPrep wrote:

Bunuel wrote:

If x is a positive number and 1/2 the square root of x is the cube root of x, then x =

A. 64
B. 32
C. 16
D. 4
E. 1

We can create the equation:

(1/2)√x = ^3√x

(½)x^(½) = x^(⅓)

We can raise each side to the 6th power, obtaining:

[(½)^6](x^3) = x^2

Dividing each side by x^2 (which is possible because x is positive), we have:

(1/64)x = 1

x = 64

Answer: A

This solution.. clear the concept

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bumpbot

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Re: . If x is a positive number and 1/2 the square root of x is the cube [#permalink]

10 Jun 2023, 12:32

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Re: . If x is a positive number and 1/2 the square root of x is the cube [#permalink]

10 Jun 2023, 12:32

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