Respuesta :

It’s gonna be radical 10x/ 4x.
Answer: [tex]\frac{\sqrt{10x}}{4x}[/tex]

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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)

[tex]\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{5}*\sqrt{8x}}{\sqrt{8x}*\sqrt{8x}}[/tex]

[tex]\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{5*8x}}{\sqrt{8x*8x}}[/tex]

[tex]\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{40x}}{\sqrt{(8x)^2}}[/tex]

[tex]\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{4*10x}}{8x}[/tex]

[tex]\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{4}*\sqrt{10x}}{8x}[/tex]

[tex]\frac{\sqrt{5}}{\sqrt{8x}} = \frac{2*\sqrt{10x}}{8x}[/tex]

[tex]\frac{\sqrt{5}}{\sqrt{8x}} = \frac{\sqrt{10x}}{4x}[/tex]

where x > 0 for each step shown above

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

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