Question

How do you rationalize `10/sqrt8`?

Answer 1

See a solution process below:

Explanation:

To rationalize a fraction you need to multiply the fraction by the appropriate form of `1` to eliminate the radical in the denominator:

`sqrt(8)/sqrt(8) * 10/sqrt(8) => (sqrt(8) * 10) /(sqrt(8) * sqrt(8)) => (10sqrt(8))/8`

We can simplify this expression as:

`(10sqrt(8))/8 => (10sqrt(4 * 2))/8 => (10sqrt(4)sqrt(2))/8 => (10 * 2sqrt(2))/8 => (20sqrt(2))/8 =>`

`(4 * 5sqrt(2))/(4 * 2) => (color(red)(cancel(color(black)(4))) * 5sqrt(2))/(color(red)(cancel(color(black)(4))) * 2) => (5sqrt(2))/2`