Question

Simplify the radical expression attached below.

Answer 1

It’s gonna be radical 10x/ 4x.

Answer 2

Answer:
`(√(10x))/(4x)`

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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)


`(√(5))/(√(8x)) = (√(5)*√(8x))/(√(8x)*√(8x))`


`(√(5))/(√(8x)) = (√(5*8x))/(√(8x*8x))`


`(√(5))/(√(8x)) = (√(40x))/(√((8x)^2))`


`(√(5))/(√(8x)) = (√(4*10x))/(8x)`


`(√(5))/(√(8x)) = (√(4)*√(10x))/(8x)`


`(√(5))/(√(8x)) = (2*√(10x))/(8x)`


`(√(5))/(√(8x)) = (√(10x))/(4x)`

where x > 0 for each step shown above

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