Question

How do you rationalize `sqrt22/sqrt33`?

Answer 1

Write it as:
`sqrt(22)/sqrt(33)=sqrt(22/33)=` divide both by `11` `=sqrt(2/3)`
Now:
`sqrt(2/3)=sqrt(2)/sqrt(3)=sqrt(2)/sqrt(3)*sqrt(3)/sqrt(3)=sqrt(6)/3`

Or:
`sqrt(22)/sqrt(33)*sqrt(33)/sqrt(33)=sqrt(22*33)/33=sqrt((2*11)(3*11))/33=sqrt(6*11^2)/33=11/33sqrt(6)=sqrt(6)/3`