Question

How do you simplify `(2sqrt(7)+35)/[sqrt(7)]`?

Answer 1

`2+5sqrt7`

Explanation:

It would help if there was something that we could cancel out. At first glance, there is a `sqrt7` in the numerator and the denominator, so lets see if we can do something about that. If we factor `35` we get;

`35=5*7`

But the `7` can be further factored by taking the square root.

`7=sqrt7^2=sqrt7*sqrt7`

So `35` becomes;

`35=5*sqrt7*sqrt7`

Now we can start simplifying the expression.

`(2sqrt7 + 35)/sqrt7=(2sqrt7 + 5*sqrt7*sqrt7)/sqrt7`

Move the `sqrt7` out of the numerator.

`(sqrt7(2+5sqrt7))/sqrt7`

Now the `sqrt7`s cancel and we have;

`(cancelsqrt7(2+5sqrt7))/cancelsqrt7=2+5sqrt7`