Help with solving equation: 4 = x sqrt x

[LynaEllrodt]

4 = x sqrt x

The answer in the book is 1/16 but I can not come up with the same answer.. Please help.. Thank you

 

[galactus]

\(\displaystyle \L\\4=x\sqrt{x}\)

\(\displaystyle \L\\4=x^{\frac{3}{2}}\)

\(\displaystyle \L\\x=4^{\frac{2}{3}}=2\cdot{2^{\frac{1}{3}}}\approx{2.52}\)

Not 1/16

 

[TchrWill]

Given 4 = x sqrt x

The answer in the book is 1/16 but I can not come up with the same answer.. Please help.. Thank you

Just another viewpoint:

4 = xsqrtx

Squaring both sides yields 16 = x^3

The cube root of 16 is 2.5198421...

 

[tkhunny]

Please don't rely on the answers in the book. Once you gain some personal confidence, you can check the answers. No need to let them beat up on you.

 

[Denis]

IF the answer IS 1/16, then you (or the book) typoed the equation:
should be sqrt(x) / x = 4

square both sides:
x / x^2 = 16
1 / x = 16
x = 1/16