Simplifying a radical to solve a problem

Question

$$ L = \sqrt{(x+8)^2 + \left(\dfrac{10(x+8)}{x}\right)^2} $$ $$ L = \sqrt{(x+8)^2 + \dfrac{100(x+8)^2}{x^2}} $$ $$ L = \sqrt{(x+8)^2\left(1 + \dfrac{100}{x^2}\right)} $$ $$ L = (x+8)\sqrt{1 + \dfrac{100}{x^2}} $$ Here am stuck, the answer is $$ L = \frac{(x+8)}{x}\sqrt{x^2 + 100} $$

Answer 1

Find the common denominator in the radicand:

$$\begin{align} L = (x+8)\sqrt{1 + \dfrac{100}{x^2}} & = (x+8)\sqrt{\dfrac{x^2 + 100}{x^2}} \\ \\ & = \dfrac{(x+8)}{x}\sqrt{x^2 + 100} \end{align}$$