Question

How do you rationalize the denominator and simplify `sqrt(5/10)`?

Answer 1

`sqrt2/2`

Explanation:

First, we can simplify what's in the big root sign:
`sqrt(5/10)=sqrt(1/2)`
And we can split the big root sign into two smaller ones:
`=sqrt1/sqrt2`
`=1/sqrt2`
Now we do something unexpected, and put another term into the equation.
`=1/sqrt2*sqrt2/sqrt2`
We can do this because `sqrt2/sqrt2` is just 1, and anything times 1 is itself. Moreover we do this because the question asks us to rationalise the denominator, asking to remove any root signs.
`=sqrt2/(sqrt2*sqrt2)`
`=sqrt2/2`