Question

How do you simplify `root5(12)/(4root5(-4))`?

Answer 1

`(root5(12))/(4root5(-4))=color(red)(-root5(3)/4)`

Explanation:

`root5(12)/(4root5(-4)`

`color(white)("XXX")=(root5(3) * cancel(root5(4)))/(4 * root5(-1) * cancel(root5(4)))`

`color(white)("XXX")=root5(3)/(4 * (-1))`

`color(white)("XXX")=-root5(3)/4`

Answer 2

`color(red)(=-root5(3)/4` or `color(red)(=-0.311432734`

Explanation:

`root5(12)/(4root5(-4)`

`:.=(root5(3) * cancelroot5(4)^color(red)1)/(4 * cancelroot5(4)^color(red)1* root5(-1) )`

`:.=root5(3)/(4 * (-1))`

`:.color(red)(=-root5(3)/4`

`:.color(red)(=-0.311432734`

Alternative method:

`:.=12^(1/5)/(4*(-4)^(1/5))`

`:.=12^0.2/(4*(-4)^0.2)`

using the calculator:

`:.=1.64375183/(4*-1.319507911)`

`:.=1.64375183/(-5.278031644)`

`:.color(red)(=-0.311432734`