Question

How do you rationalize the denominator and simplify `sqrt 55/sqrt10`?

Answer 1

To keep the numbers smaller, try to reduce first. Both `55` and `10` are divisible by `5`. Use that to write:

`sqrt55/sqrt10 = (sqrt5sqrt11)/(sqrt5sqrt2)= sqrt11/sqrt2`

Now rationalize tlhe denominator by multiplying by `1` in the form: `sqrt2/sqrt2`

`sqrt55/sqrt10 = sqrt11/sqrt2 sqrt2/sqrt2 = sqrt22/2` and we're done.

Notice

I find it worth trying to reduce first. If you don't reduce first, then you'll still get the correct answer, and it hooks like this:

`sqrt55/sqrt10 =sqrt55/sqrt10 sqrt10/sqrt10 = sqrt550/10`

`sqrt55/sqrt10 = sqrt550/10 = sqrt(55*10)/10 = sqrt(5*11*2*5)/10 = sqrt (25*22)/10 = (5sqrt22)/10 = sqrt22/2`