Question

How do you simplify `sqrt(a^2/b^2)`?

Answer 1

Use the rule `sqrt(x/y)=sqrtx/sqrty`

Explanation:

`=sqrta^2/sqrtb^2=|a|/|b|`

Since `a^2/b^2` is necessarily positive, we must assure that `a/b` is non-negative as well (that's why the absolute bars).

Or you could have used `x^2/y^2=(x/y)^2`

`=sqrt((a/b))^2=|a/b|`