Question

cubic and cube root functions and equations
which equation results from isolating a radical term and squaring both sides of the equation for the equation
$sqrt{x+8}+sqrt{x}=8$
$x+6=64-x$
$x+6=64+x+16sqrt{x}$
$x+6=64+x-16sqrt{x}$
$x+6=64+x$

Explanation:

Step1: Isolate the radical term

$\sqrt{x+6} = 8 - \sqrt{x}$

Step2: Square both sides

$(\sqrt{x+6})^2 = (8 - \sqrt{x})^2$

Step3: Expand both sides

$x+6 = 8^2 - 2\cdot8\cdot\sqrt{x} + (\sqrt{x})^2$

Step4: Simplify the expression

$x+6 = 64 - 16\sqrt{x} + x$

Answer:

$x + 6 = 64 + x - 16\sqrt{x}$