Question

8.6 solve radical equations (homework)
score: 12/16 answered: 12/16
question 13
solve.
\\(\sqrt3{5z - 3}+7 = 9\\)
\\(z =\\)

Explanation:

Step1: Isolate the cube - root term

Subtract 7 from both sides of the equation $\sqrt[3]{5z - 3}+7 = 9$.
$\sqrt[3]{5z - 3}=9 - 7$
$\sqrt[3]{5z - 3}=2$

Step2: Eliminate the cube - root

Cube both sides of the equation.
$(\sqrt[3]{5z - 3})^3=2^3$
$5z-3 = 8$

Step3: Solve for z

Add 3 to both sides: $5z=8 + 3$, so $5z=11$.
Then divide both sides by 5: $z=\frac{11}{5}=2.2$

Answer:

$z = 2.2$