Question

solving equations containing two radicals
solving equations containing two radicals
this is a multi-part item.
which of the following occurs within the solution process for $sqrt3{5x + 3} - sqrt3{4x} = 0$

• cubing both sides twice
• squaring both sides once
• cubing both sides once
• squaring both sides twice

the potential solution of $sqrt3{5x + 3} - sqrt3{4x} = 0$ is $x = \square$

Explanation:

Step1: Isolate one radical

$\sqrt[3]{5x+3} = \sqrt[3]{4x}$

Step2: Cube both sides once

$(\sqrt[3]{5x+3})^3 = (\sqrt[3]{4x})^3$
$5x + 3 = 4x$

Step3: Solve for x

$5x - 4x = -3$
$x = -3$

Answer:

1. cubing both sides once
2. $x = -3$