422 What is the solution of $$ \sqrt[3]{x+8}=-4 $$ ? $$ x=-72 $$

Question

UpStudy AI · Accepted Answer

Yes, your solution is correct. Here's a step-by-step explanation of how to solve the equation:

$$
\sqrt[3]{x + 8} = -4
$$

**Step 1: Eliminate the Cube Root**

To remove the cube root, you can cube both sides of the equation:

$$
\left( \sqrt[3]{x + 8} \right)^3 = (-4)^3
$$

This simplifies to:

$$
x + 8 = -64
$$

**Step 2: Solve for $$ x $$**

Subtract 8 from both sides to isolate $$ x $$:

$$
x = -64 - 8
$$
$$
x = -72
$$

**Final Answer:**
$$
x = -72
$$

Your solution correctly finds that $$ x = -72 $$ satisfies the original equation.
$$ x = -72 $$

422
What is the solution of ?