If √(x+8) = 4, what is the value of x after solving the equation?

Understand the Problem

The question is asking us to solve the equation \sqrt{x+8} = 4 for the variable x. To solve it, we will square both sides to eliminate the square root, leading us to an equation that can be simplified to find the value of x.

Answer

$x = 8$

Steps to Solve

Square both sides of the equation

To eliminate the square root, we will square both sides of the equation:

$$ (\sqrt{x+8})^2 = 4^2 $$

This simplifies to:

$$ x + 8 = 16 $$

Isolate the variable x

Next, we need to solve for $x$ by isolating it. We can do this by subtracting 8 from both sides:

$$ x + 8 - 8 = 16 - 8 $$

This simplifies to:

$$ x = 8 $$

Check the solution

Finally, we should check our solution by substituting $x = 8$ back into the original equation to verify it works:

$$ \sqrt{8+8} = 4 $$

Simplifying gives:

$$ \sqrt{16} = 4 $$

Since this statement is true, our solution is confirmed.

The final answer is: $x = 8$.

More Information

When solving equations involving square roots, it's crucial to check your solutions, as squaring both sides can introduce extraneous solutions that don't satisfy the original equation.

Tips

Forgetting to check the solution after finding $x$ can lead to accepting a wrong answer.
Miscalculating during the squaring process can change the outcome. Always double-check calculations.

Thank you for voting!