Question

How do you simplify `5/sqrt5`?

Answer 1

`sqrt(5)`

Explanation:

Whenever you have a surd as the denominator, we rationalise it, meaning we multiply it and the numerator (because multiplying any number by 1 doesn't change it) by itself to get a 'normal' number on the bottom. So in this case we would do

`5/sqrt(5) xx sqrt(5)/sqrt(5) = (5sqrt(5))/5`

*notice how `sqrt(5)/sqrt(5)=1` so by multiplying `5/sqrt(5)` we are to changing it *

Then we would simplify `(5sqrt(5))/5` to get `(1sqrt(5))/1` which equals to `sqrt(5)`

Answer 2

`sqrt5`

Explanation:

`color(blue)(5/sqrt(5)`

We need to simplify this.The first thing we need to know is that, we need to rationalize the denominator.

So, multiply the denominator and numerator with `sqrt5`

`rarr5/sqrt5*sqrt5/sqrt5`

`rarr(5sqrt5)/5`

`rarr(cancel5sqrt5)/cancel5`

`color(green)(rArrsqrt5`

Hope this helps... :)