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
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