Question

How do you simplify `(5sqrt3)/(6sqrt10)`?

Answer 1

`sqrt30/12`

Explanation:

`"using the "color(blue)"laws of radicals"`

`•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)`

`•color(white)(x)sqrtaxxsqrta=a`

`"to simplify we require to remove the radical from the "`
`"denominator"`

`"this is achieved by multiplying numerator/denominator"`
`"by "sqrt10`

`rArr(5sqrt3)/(6sqrt10)xxsqrt10/sqrt10`

`=(5xxsqrt(3xx10))/(6xxsqrt(10xx10))`

`=(5xxsqrt30)/(6xxsqrt100)=(cancel(5)^1xxsqrt30)/(cancel(60)^(12))=sqrt30/12`