To solve the equation [tex]\(\sqrt{x + 6} = 16\)[/tex], follow these steps:
1. Square both sides of the equation to eliminate the square root. This is done because squaring is the inverse operation of taking the square root.
[tex]\[
(\sqrt{x + 6})^2 = 16^2
\][/tex]
2. Simplify both sides of the equation. The left side simplifies because the square of a square root cancels out, and the right side is simply the square of 16.
[tex]\[
x + 6 = 256
\][/tex]
3. Solve for [tex]\(x\)[/tex] by isolating it. To do this, subtract 6 from both sides of the equation.
[tex]\[
x + 6 - 6 = 256 - 6
\][/tex]
Which simplifies to:
[tex]\[
x = 250
\][/tex]
So, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\sqrt{x + 6} = 16\)[/tex] is [tex]\(x = 250\)[/tex].
