Question

How do you simplify `\frac { 4} { \sqrt { 5} - 7}`?

Answer 1

See a solution process below:

Explanation:

We will simplify the expression by rationalizing the denominator, or, in other words, removing the radical from the denominator. We will multiply the expression by the appropriate form of `1` to eliminate the radical while keeping the value of the fraction the same:

`(sqrt(5) + 7)/(sqrt(5) + 7) xx 4/(sqrt(5) - 7) =>`

`(4(sqrt(5) + 7))/((sqrt(5) + 7)(sqrt(5) - 7)) =>`

`(4(sqrt(5) + 7))/((sqrt(5))^2 - 7sqrt(5) + 7sqrt(5) - 7^2) =>`

`(4(sqrt(5) + 7))/(5 - 0 - 49) =>`

`(4(sqrt(5) + 7))/(-44) =>`

`-(4(sqrt(5) + 7))/(4 xx 11) =>`

`-(color(red)(cancel(color(black)(4)))(sqrt(5) + 7))/(color(red)(cancel(color(black)(4))) xx 11) =>`

`-(sqrt(5) + 7)/11`

Answer 2

`-0.84` to the nearest 2 decimal places

Explanation:

`4/(sqrt5-7)`

`:.=4/(2.236067978-7)`

`:.=4/-4.763932023`

`:.=-0.839642543`

`:.=-0.84` to the nearest 2 decimal places