Question

How do you simplify `8 sqrt (19s) - 8 sqrt(10d) - 4 sqrt( 19s) - 8 sqrt (10d)`?

Answer 1

`4sqrt(19s)-16sqrt(10d)`

Explanation:

Let's first look at the terms within the square roots themselves:

`19s` and `10d`

There is nothing within the roots that can be simplified - no squares under the root that can be extracted (unlike, for example, `sqrt4` which equals 2).

So what we're really talking about here is two complicated looking terms: `sqrt(19s)` and `sqrt(10d)` and different coefficients of them. So how about if we change the complicated looking terms and substitute in something easier to work with:

`A=sqrt(19s)`
`B=sqrt(10d)`

which gets us:

`8A-8B-4A-8B`

which gives us:

`4B-16B`

and now we can put in the original terms:

`4sqrt(19s)-16sqrt(10d)`