Question

How do you rationalize the dominator and simplify for the square root of 35 over the square root of 55?

Answer 1

`sqrt(77)/11`

Explanation:

Your expression is `sqrt(35)/sqrt(55)`. Since you can always mutiply an expression by `1` without changing its value, and you can see `1` as any number divided by itself, we have

`sqrt(35)/sqrt(55)=sqrt(35)/sqrt(55)*1 = sqrt(35)/sqrt(55)*sqrt(55)/sqrt(55)`

Doing the multiplications (remember that `sqrt(a)*sqrt(b)=sqrt(a*b)`), we have

`sqrt(35*55)/sqrt(55^2)`

And of course `sqrt(a^2)=a` (if `a` is positive), so we have

`sqrt(1925)/55`.

Finally, we can factor `1925` with prime numbers, and we have

`1925 = 5^2*7*11`, and so `sqrt(1925)=sqrt(5^2*7*11)=5sqrt(7*11)`, and `5` and `55` cancel out.