Question

cubic and cube root functions and equations
which statement describes how to solve $sqrt{3x + 4} = sqrt{3x} + 4$
square both sides once and then solve the resulting quadratic equation.
square both sides twice and then solve the resulting quadratic equation.
square both sides once and then solve the resulting linear equation.
square both sides twice and then solve the resulting linear equation.

Explanation:

Step1: Identify equation type

We have the equation $\sqrt{3x + 4} = \sqrt{3x} + 4$, with square roots on both sides.

Step2: Square both sides first

Square each side to eliminate outer square roots:
$$(\sqrt{3x + 4})^2 = (\sqrt{3x} + 4)^2$$
$$3x + 4 = 3x + 8\sqrt{3x} + 16$$

Step3: Simplify to isolate remaining root

Simplify the equation to get the remaining square root alone:
$$3x + 4 - 3x - 16 = 8\sqrt{3x}$$
$$-12 = 8\sqrt{3x}$$

Step4: Recognize need for second square

To eliminate the remaining square root, we need to square both sides again, then solve the resulting linear equation.

Answer:

Square both sides twice and then solve the resulting linear equation.