# How do you solve 4x^(3/2) - 5 = 103 and find any extraneous solutions?

May 31, 2016

$x = 2 \textcolor{w h i t e}{.} \sqrt[3]{99}$

Not sure where the extraneous solutions come from!

#### Explanation:

$4 {x}^{\frac{3}{2}} = 108$

Write as : $4 \sqrt{{x}^{3}} = 108$

Divide both sides by 4

$\sqrt{{x}^{3}} = 27$

square both sides

${x}^{3} = 792 \text{ }$

cube root both sides

$x = \sqrt[3]{792} = \sqrt[3]{{2}^{3} \times {3}^{2} \times 11} \text{ "larr" prime factors}$

$x = 2 \textcolor{w h i t e}{.} \sqrt[3]{99}$