Question

add. assume all variables are greater than or equal to one.\\(\sqrt{16x - 16} + \sqrt{4x - 4}\\)\\(\sqrt{16x - 16} + \sqrt{4x - 4} = \\)\\(\text{(simplify your answer. type an exact answer, using radicals as nee}\\)

Explanation:

Step1: Factor out common terms inside radicals

For $\sqrt{16x - 16}$, factor out 16: $\sqrt{16(x - 1)} = \sqrt{16}\cdot\sqrt{x - 1} = 4\sqrt{x - 1}$ (since $x\geq1$, $\sqrt{x - 1}$ is defined).
For $\sqrt{4x - 4}$, factor out 4: $\sqrt{4(x - 1)} = \sqrt{4}\cdot\sqrt{x - 1} = 2\sqrt{x - 1}$.

Step2: Combine like terms

Now we have $4\sqrt{x - 1} + 2\sqrt{x - 1}$. Since both terms have $\sqrt{x - 1}$, we add the coefficients: $(4 + 2)\sqrt{x - 1} = 6\sqrt{x - 1}$.

Answer:

$6\sqrt{x - 1}$