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

Question

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

msk0657 · Answer

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.

freedomfox2121 · Answer

Hello,

Could someone please explain how to solve this algebraically?

Thanks in advance.

cptholt · Answer

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

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

(x) ^ 1/6 = 2

x = 64

freedomfox2121 · Answer

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.

yvankd · Answer

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

shashankism · Answer

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

ScottTargetTestPrep · Answer

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:

(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

BlueRocketAsh · Answer

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

ScottTargetTestPrep · Answer

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

philipssonicare · Answer

\frac{√x}{2}=\sqrt {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

RiyadhArifin237 · Answer

This solution.. clear the concept

Posted from my mobile device

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

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