Question

What is the simplest radical form of `sqrt(5) / sqrt(6)`?

Answer 1

`sqrt(5)/sqrt(6)=sqrt(5/6)=sqrt(0.8333...)`

Explanation:

When dealing with positive numbers `p` and `q`, it's easy to prove that
`sqrt(p)*sqrt(q)=sqrt(p*q)`
`sqrt(p)/sqrt(q)=sqrt(p/q)`

For instance, the latter can be proven by squaring the left part:
`(sqrt(p)/sqrt(q))^2=[sqrt(p)*sqrt(p)]/[sqrt(q)*sqrt(q)]=p/q`
Therefore, by definition of a square root,
from
`p/q=(sqrt(p)/sqrt(q))^2`
follows
`sqrt(p/q)=sqrt(p)/sqrt(q)`

Using this, the expression above can be simplified as
`sqrt(5)/sqrt(6)=sqrt(5/6)=sqrt(0.8333...)`