Question

How do you simplify `(2sqrt(5x))/sqrt(25x^2)`?

Answer 1

See the solution process below:

Explanation:

We can rewrite this expression as:

`(2sqrt(5x))/(sqrt(5x)sqrt(5x))`

We can next cancel common terms in the numerator and denominator:

`(2color(red)(cancel(color(black)(sqrt(5x)))))/(color(red)(cancel(color(black)(sqrt(5x)))sqrt(5x))) =>`

`2/sqrt(5x)`

Now we can rationalize the denominator by multiplying the fraction by the appropriate form of 1:

`sqrt(5x)/sqrt(5x) xx 2/sqrt(5x) =>`

`(sqrt(5x) xx 2)/(sqrt(5x) xx sqrt(5x)) =>`

`(2sqrt(5x))/(5x)`