Question

Simplify the radical expression attached below.

Answer 1

Answer: $\frac{\sqrt{10x}}{4x}$

===========================================================

Work Shown:

The idea is to multiply top and bottom by sqrt(8x) to make the denominator rational (ie get rid of the square root)

$\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{5}*\sqrt{8x}}{\sqrt{8x}*\sqrt{8x}}$

$\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{5*8x}}{\sqrt{8x*8x}}$

$\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{40x}}{\sqrt{(8x)^2}}$

$\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{4*10x}}{8x}$

$\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{4}*\sqrt{10x}}{8x}$

$\frac{\sqrt{5}}{\sqrt{8x}} = \frac{2*\sqrt{10x}}{8x}$

$\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{10x}}{4x}$

where x > 0 for each step shown above

note: refresh the page if the math symbols do not show up

Answer 2

It’s gonna be radical 10x/ 4x.